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- Derivada de una función implícitamente dada
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- Análisis de la función gráfica
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- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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- Derivada de:
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Derivada de -П/3
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Derivada de (-п/3)
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Derivada de (п/3)-(п/4)
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Derivada de П/3*(0,5(3t^2-t))
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Expresiones idénticas
- -(xsin siete x)^ tres /((uno -x^ dos)^((uno / dos))+ tres *7(sin(7x)^ dos)*(uno -x^ dos)^(uno / dos)*cos(7x))/(cos(6x)^ dos)
- menos (x seno de 7x) al cubo dividir por ((1 menos x al cuadrado ) en el grado ((1 dividir por 2)) más 3 multiplicar por 7( seno de (7x) al cuadrado ) multiplicar por (1 menos x al cuadrado ) en el grado (1 dividir por 2) multiplicar por coseno de (7x)) dividir por ( coseno de (6x) al cuadrado )
- menos (x seno de siete x) en el grado tres dividir por ((uno menos x en el grado dos) en el grado ((uno dividir por dos)) más tres multiplicar por 7( seno de (7x) en el grado dos) multiplicar por (uno menos x en el grado dos) en el grado (uno dividir por dos) multiplicar por coseno de (7x)) dividir por ( coseno de (6x) en el grado dos)
- -(xsin7x)3/((1-x2)((1/2))+3*7(sin(7x)2)*(1-x2)(1/2)*cos(7x))/(cos(6x)2)
- -xsin7x3/1-x21/2+3*7sin7x2*1-x21/2*cos7x/cos6x2
- -(xsin7x)³/((1-x²)^((1/2))+3*7(sin(7x)²)*(1-x²)^(1/2)*cos(7x))/(cos(6x)²)
- -(xsin7x) en el grado 3/((1-x en el grado 2) en el grado ((1/2))+3*7(sin(7x) en el grado 2)*(1-x en el grado 2) en el grado (1/2)*cos(7x))/(cos(6x) en el grado 2)
- -(xsin7x)^3/((1-x^2)^((1/2))+37(sin(7x)^2)(1-x^2)^(1/2)cos(7x))/(cos(6x)^2)
- -(xsin7x)3/((1-x2)((1/2))+37(sin(7x)2)(1-x2)(1/2)cos(7x))/(cos(6x)2)
- -xsin7x3/1-x21/2+37sin7x21-x21/2cos7x/cos6x2
- -xsin7x^3/1-x^2^1/2+37sin7x^21-x^2^1/2cos7x/cos6x^2
- -(xsin7x)^3 dividir por ((1-x^2)^((1 dividir por 2))+3*7(sin(7x)^2)*(1-x^2)^(1 dividir por 2)*cos(7x)) dividir por (cos(6x)^2)
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Expresiones semejantes
- -(xsin7x)^3/((1+x^2)^((1/2))+3*7(sin(7x)^2)*(1-x^2)^(1/2)*cos(7x))/(cos(6x)^2)
- -(xsin7x)^3/((1-x^2)^((1/2))+3*7(sin(7x)^2)*(1+x^2)^(1/2)*cos(7x))/(cos(6x)^2)
- (xsin7x)^3/((1-x^2)^((1/2))+3*7(sin(7x)^2)*(1-x^2)^(1/2)*cos(7x))/(cos(6x)^2)
- -(xsin7x)^3/((1-x^2)^((1/2))-3*7(sin(7x)^2)*(1-x^2)^(1/2)*cos(7x))/(cos(6x)^2)
Derivada de la función/
-(xsin7x)^3/((1-x^2)^((1/2))+3*7(sin(7x)^2)*(1-x^2)^(1/2)*cos(7x))/(cos(6x)^2)
Derivada de -(xsin7x)^3/((1-x^2)^((1/2))+3*7(sin(7x)^2)*(1-x^2)^(1/2)*cos(7x))/(cos(6x)^2)
Solución
Ha introducido
[src]
/ 3 \
| -(x*sin(7*x)) |
|-----------------------------------------------|
| ________ ________ |
| / 2 2 / 2 |
\\/ 1 - x + 21*sin (7*x)*\/ 1 - x *cos(7*x)/
-------------------------------------------------
2
cos (6*x)
$$\frac{- \left(x \sin{\left(7 x \right)}\right)^{3} \frac{1}{\sqrt{1 - x^{2}} \cdot 21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + \sqrt{1 - x^{2}}}}{\cos^{2}{\left(6 x \right)}}$$
((-(x*sin(7*x))^3)/(sqrt(1 - x^2) + ((21*sin(7*x)^2)*sqrt(1 - x^2))*cos(7*x)))/cos(6*x)^2
Primera derivada
[src]
/ / 2 ________ \ ________ \
3 3 | x | 21*x*sin (7*x) / 2 | / 2 3 |
x *sin (7*x)*|----------- - |- -------------- + 294*\/ 1 - x *cos(7*x)*sin(7*x)|*cos(7*x) + 147*\/ 1 - x *sin (7*x)|
| ________ | ________ | |
| / 2 | / 2 | | 2 2
\\/ 1 - x \ \/ 1 - x / / x *sin (7*x)*(3*sin(7*x) + 21*x*cos(7*x))
- ------------------------------------------------------------------------------------------------------------------------ - -----------------------------------------------
2 ________ ________
/ ________ ________ \ / 2 2 / 2
| / 2 2 / 2 | \/ 1 - x + 21*sin (7*x)*\/ 1 - x *cos(7*x) 3 3
\\/ 1 - x + 21*sin (7*x)*\/ 1 - x *cos(7*x)/ 12*x *sin (7*x)*sin(6*x)
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------
2 / ________ ________ \
cos (6*x) | / 2 2 / 2 | 3
\\/ 1 - x + 21*sin (7*x)*\/ 1 - x *cos(7*x)/*cos (6*x)
$$- \frac{12 x^{3} \sin^{3}{\left(7 x \right)} \sin{\left(6 x \right)}}{\left(\sqrt{1 - x^{2}} \cdot 21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + \sqrt{1 - x^{2}}\right) \cos^{3}{\left(6 x \right)}} + \frac{- \frac{x^{2} \left(21 x \cos{\left(7 x \right)} + 3 \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}} \cdot 21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + \sqrt{1 - x^{2}}} - \frac{x^{3} \sin^{3}{\left(7 x \right)} \left(\frac{x}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} - \left(- \frac{21 x \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 294 \sqrt{1 - x^{2}} \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right) \cos{\left(7 x \right)}\right)}{\left(\sqrt{1 - x^{2}} \cdot 21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + \sqrt{1 - x^{2}}\right)^{2}}}{\cos^{2}{\left(6 x \right)}}$$
Segunda derivada
[src]
/ / 2\ \
| | 2 / ________ \ / 2 ________ ________ 2 2 \ 3 ________ / ________ / ________ \ \ | / / ________ / ________ \ \ \ |
| | 1 x 2 | / 2 x*sin(7*x)| | sin (7*x) / 2 2 / 2 2 x *sin (7*x) 28*x*cos(7*x)*sin(7*x)| 147*x*sin (7*x) / 2 2 | x / 2 3 | / 2 x*sin(7*x)| | | | | x / 2 3 | / 2 x*sin(7*x)| | | |
| |----------- + ----------- - 147*sin (7*x)*|- 14*\/ 1 - x *cos(7*x) + -----------| + 21*|----------- - 98*\/ 1 - x *cos (7*x) + 98*\/ 1 - x *sin (7*x) + ------------ + ----------------------|*cos(7*x) - --------------- + 3087*\/ 1 - x *sin (7*x)*cos(7*x) 2*|----------- + 147*\/ 1 - x *sin (7*x) + 21*|- 14*\/ 1 - x *cos(7*x) + -----------|*cos(7*x)*sin(7*x)| | | x*|----------- + 147*\/ 1 - x *sin (7*x) + 21*|- 14*\/ 1 - x *cos(7*x) + -----------|*cos(7*x)*sin(7*x)|*sin(7*x)| |
| | ________ 3/2 | ________| | ________ 3/2 ________ | ________ | ________ | ________| | | | | ________ | ________| | | |
| | / 2 / 2\ | / 2 | | / 2 / 2\ / 2 | / 2 | / 2 | / 2 | | | | | / 2 | / 2 | | | / ________ / ________ \ \ |
| 2 2 |\/ 1 - x \1 - x / \ \/ 1 - x / \\/ 1 - x \1 - x / \/ 1 - x / \/ 1 - x \\/ 1 - x \ \/ 1 - x / / | / 2 \ |3*(7*x*cos(7*x) + sin(7*x)) \\/ 1 - x \ \/ 1 - x / / | | x / 2 3 | / 2 x*sin(7*x)| | |
| x *sin (7*x)*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------| 2 2 | 3*sin (6*x)| 24*x*|--------------------------- + ---------------------------------------------------------------------------------------------------------------------|*sin(6*x)*sin(7*x) 6*x*(7*x*cos(7*x) + sin(7*x))*|----------- + 147*\/ 1 - x *sin (7*x) + 21*|- 14*\/ 1 - x *cos(7*x) + -----------|*cos(7*x)*sin(7*x)|*sin(7*x)|
| | 2 3/2 | 72*x *sin (7*x)*|1 + -----------| | ________ / 2\ / 2 \ | | ________ | ________| | |
| / 2 \ | -1 + x / 2\ / 2 \ | | 2 | | / 2 \1 - x /*\1 + 21*sin (7*x)*cos(7*x)/ | | / 2 | / 2 | | |
|3*\- 3*(7*x*cos(7*x) + sin(7*x)) + (7*x*cos(7*x) + sin(7*x))*sin(7*x) + 7*x*(-2*cos(7*x) + 7*x*sin(7*x))*sin(7*x) + 7*x*(7*x*cos(7*x) + sin(7*x))*cos(7*x)/ \ \1 - x / *\1 + 21*sin (7*x)*cos(7*x)/ / \ cos (6*x) / \ \/ 1 - x / \\/ 1 - x \ \/ 1 - x / / |
x*|------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------|*sin(7*x)
| ________ 2 ________ cos(6*x) / 2 \ / 2\ |
| / 2 1 + 21*sin (7*x)*cos(7*x) / 2 \1 + 21*sin (7*x)*cos(7*x)/*\-1 + x / |
\ \/ 1 - x \/ 1 - x /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2 \ 2
\1 + 21*sin (7*x)*cos(7*x)/*cos (6*x)
$$\frac{x \left(\frac{x^{2} \left(\frac{\frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{147 x \sin^{3}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 3087 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} - 147 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)} + 21 \left(\frac{x^{2} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{28 x \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 98 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} - 98 \sqrt{1 - x^{2}} \cos^{2}{\left(7 x \right)} + \frac{\sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right) \cos{\left(7 x \right)} + \frac{1}{\sqrt{1 - x^{2}}}}{x^{2} - 1} - \frac{2 \left(\frac{x}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} + 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right)^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right)}\right) \sin^{2}{\left(7 x \right)}}{21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1} - \frac{72 x^{2} \left(\frac{3 \sin^{2}{\left(6 x \right)}}{\cos^{2}{\left(6 x \right)}} + 1\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - \frac{24 x \left(\frac{x \left(\frac{x}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} + 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)}}{\left(1 - x^{2}\right) \left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right)} + \frac{3 \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right)}{\sqrt{1 - x^{2}}}\right) \sin{\left(6 x \right)} \sin{\left(7 x \right)}}{\cos{\left(6 x \right)}} + \frac{6 x \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \left(\frac{x}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} + 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)}}{\left(x^{2} - 1\right) \left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right)} + \frac{3 \left(7 x \left(7 x \sin{\left(7 x \right)} - 2 \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} + 7 x \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \cos{\left(7 x \right)} - 3 \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right)^{2} + \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)}\right)}{\sqrt{1 - x^{2}}}\right) \sin{\left(7 x \right)}}{\left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right) \cos^{2}{\left(6 x \right)}}$$
Tercera derivada
[src]
/ / / 2\ \ \
| | | 2 / ________ \ / 2 ________ ________ 2 2 \ 3 ________ / ________ / ________ \ \ | | |
| | | 1 x 2 | / 2 x*sin(7*x)| | sin (7*x) / 2 2 / 2 2 x *sin (7*x) 28*x*cos(7*x)*sin(7*x)| 147*x*sin (7*x) / 2 2 | x / 2 3 | / 2 x*sin(7*x)| | | | |
| | |----------- + ----------- - 147*sin (7*x)*|- 14*\/ 1 - x *cos(7*x) + -----------| + 21*|----------- - 98*\/ 1 - x *cos (7*x) + 98*\/ 1 - x *sin (7*x) + ------------ + ----------------------|*cos(7*x) - --------------- + 3087*\/ 1 - x *sin (7*x)*cos(7*x) 2*|----------- + 147*\/ 1 - x *sin (7*x) + 21*|- 14*\/ 1 - x *cos(7*x) + -----------|*cos(7*x)*sin(7*x)| | | |
| / 3 \ / 2\ | | ________ 3/2 | ________| | ________ 3/2 ________ | ________ | ________ | ________| | | | |
| | 3 / 2 2 3 2 2 ________ 2 \ 3 / 2 ________ ________ 2 2 \ ________ ________ 2 3 / ________ \ 2 / ________ / ________ \ \ / ________ / ________ \ \ / 2 / ________ \ / 2 ________ ________ 2 2 \ 3 ________ \| | 2 / ________ \ / 2 ________ ________ 2 2 \ 3 ________ / ________ / ________ \ \ | | | / 2 / 2\ | / 2 | | / 2 / 2\ / 2 | / 2 | / 2 | / 2 | | | / ________ / ________ \ \ | |
| | x x | 294*x*sin (7*x) 3*x*sin (7*x) 3*x *sin (7*x) 42*cos(7*x)*sin(7*x) 294*x*cos (7*x) / 2 42*x *cos(7*x)*sin(7*x)| 49*sin (7*x) | sin (7*x) / 2 2 / 2 2 x *sin (7*x) 28*x*cos(7*x)*sin(7*x)| / 2 3 / 2 2 49*x *sin (7*x) | / 2 x*sin(7*x)| 2058*x*sin (7*x)*cos(7*x) | x / 2 3 | / 2 x*sin(7*x)| | | x / 2 3 | / 2 x*sin(7*x)| | | 1 x 2 | / 2 x*sin(7*x)| | sin (7*x) / 2 2 / 2 2 x *sin (7*x) 28*x*cos(7*x)*sin(7*x)| 147*x*sin (7*x) / 2 2 || | 1 x 2 | / 2 x*sin(7*x)| | sin (7*x) / 2 2 / 2 2 x *sin (7*x) 28*x*cos(7*x)*sin(7*x)| 147*x*sin (7*x) / 2 2 | x / 2 3 | / 2 x*sin(7*x)| | | | 2 2 |\/ 1 - x \1 - x / \ \/ 1 - x / \\/ 1 - x \1 - x / \/ 1 - x / \/ 1 - x \\/ 1 - x \ \/ 1 - x / / | | x / 2 3 | / 2 x*sin(7*x)| | | |
| |- ----------- - ----------- - 7*|- --------------- + ------------- + -------------- + -------------------- + --------------- + 2744*\/ 1 - x *cos(7*x)*sin(7*x) + -----------------------|*cos(7*x) + ------------ + 98*|----------- - 98*\/ 1 - x *cos (7*x) + 98*\/ 1 - x *sin (7*x) + ------------ + ----------------------|*sin(7*x) + 7203*\/ 1 - x *sin (7*x) - 14406*\/ 1 - x *cos (7*x)*sin(7*x) + --------------- + 343*|- 14*\/ 1 - x *cos(7*x) + -----------|*cos(7*x)*sin(7*x) + ------------------------- 2*|----------- + 147*\/ 1 - x *sin (7*x) + 21*|- 14*\/ 1 - x *cos(7*x) + -----------|*cos(7*x)*sin(7*x)| 2*|----------- + 147*\/ 1 - x *sin (7*x) + 21*|- 14*\/ 1 - x *cos(7*x) + -----------|*cos(7*x)*sin(7*x)|*|----------- + ----------- - 147*sin (7*x)*|- 14*\/ 1 - x *cos(7*x) + -----------| + 21*|----------- - 98*\/ 1 - x *cos (7*x) + 98*\/ 1 - x *sin (7*x) + ------------ + ----------------------|*cos(7*x) - --------------- + 3087*\/ 1 - x *sin (7*x)*cos(7*x)|| |----------- + ----------- - 147*sin (7*x)*|- 14*\/ 1 - x *cos(7*x) + -----------| + 21*|----------- - 98*\/ 1 - x *cos (7*x) + 98*\/ 1 - x *sin (7*x) + ------------ + ----------------------|*cos(7*x) - --------------- + 3087*\/ 1 - x *sin (7*x)*cos(7*x) 2*|----------- + 147*\/ 1 - x *sin (7*x) + 21*|- 14*\/ 1 - x *cos(7*x) + -----------|*cos(7*x)*sin(7*x)| | | x *sin (7*x)*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------| 6*x*(7*x*cos(7*x) + sin(7*x))*|----------- + 147*\/ 1 - x *sin (7*x) + 21*|- 14*\/ 1 - x *cos(7*x) + -----------|*cos(7*x)*sin(7*x)|*sin(7*x)| |
| | 3/2 5/2 | ________ 3/2 5/2 ________ ________ 3/2 | ________ | ________ 3/2 ________ | 3/2 | ________| ________ | ________ | ________| | | ________ | ________| | | ________ 3/2 | ________| | ________ 3/2 ________ | ________ || | ________ 3/2 | ________| | ________ 3/2 ________ | ________ | ________ | ________| | | | | 2 3/2 | | ________ | ________| | | |
| | / 2\ / 2\ | / 2 / 2\ / 2\ / 2 / 2 / 2\ | / 2 | / 2 / 2\ / 2 | / 2\ | / 2 | / 2 | / 2 | / 2 | | | / 2 | / 2 | | | / 2 / 2\ | / 2 | | / 2 / 2\ / 2 | / 2 || / / ________ / ________ \ \ \ | / 2 / 2\ | / 2 | | / 2 / 2\ / 2 | / 2 | / 2 | / 2 | | | | / 2 \ | -1 + x / 2\ / 2 \ | | / 2 | / 2 | | | / ________ / ________ \ \ |
| 3 3 | \1 - x / \1 - x / \ \/ 1 - x \1 - x / \1 - x / \/ 1 - x \/ 1 - x \1 - x / / \/ 1 - x \\/ 1 - x \1 - x / \/ 1 - x / \1 - x / \ \/ 1 - x / \/ 1 - x \\/ 1 - x \ \/ 1 - x / / \\/ 1 - x \ \/ 1 - x / / \\/ 1 - x \1 - x / \ \/ 1 - x / \\/ 1 - x \1 - x / \/ 1 - x / \/ 1 - x /| | | x / 2 3 | / 2 x*sin(7*x)| | | 2 2 |\/ 1 - x \1 - x / \ \/ 1 - x / \\/ 1 - x \1 - x / \/ 1 - x / \/ 1 - x \\/ 1 - x \ \/ 1 - x / / | |3*\- 3*(7*x*cos(7*x) + sin(7*x)) + (7*x*cos(7*x) + sin(7*x))*sin(7*x) + 7*x*(-2*cos(7*x) + 7*x*sin(7*x))*sin(7*x) + 7*x*(7*x*cos(7*x) + sin(7*x))*cos(7*x)/ \ \1 - x / *\1 + 21*sin (7*x)*cos(7*x)/ / \\/ 1 - x \ \/ 1 - x / / | / 2 \ | x / 2 3 | / 2 x*sin(7*x)| | / 2 \ |
| x *sin (7*x)*|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | x*|----------- + 147*\/ 1 - x *sin (7*x) + 21*|- 14*\/ 1 - x *cos(7*x) + -----------|*cos(7*x)*sin(7*x)|*sin(7*x)| 3*x *sin (7*x)*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------|*(7*x*cos(7*x) + sin(7*x)) 12*x*|------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------|*sin(6*x)*sin(7*x) 3 3 | 3*sin (6*x)| 3*x*|----------- + 147*\/ 1 - x *sin (7*x) + 21*|- 14*\/ 1 - x *cos(7*x) + -----------|*cos(7*x)*sin(7*x)|*\- 3*(7*x*cos(7*x) + sin(7*x)) + (7*x*cos(7*x) + sin(7*x))*sin(7*x) + 7*x*(-2*cos(7*x) + 7*x*sin(7*x))*sin(7*x) + 7*x*(7*x*cos(7*x) + sin(7*x))*cos(7*x)/*sin(7*x)|
| | 2 2 2 3/2 | | | ________ | ________| | | | 2 3/2 | | ________ 2 / 2 \ / 2\ | 576*x *sin (7*x)*|2 + -----------|*sin(6*x) | ________ | ________| | |
| 2 / 2 2 2 2 2 \ 2 2 2 2 2 2 2 2 2 2 | -1 + x / 2 \ / 2\ / 2\ / 2 \ | / 2 \ | | / 2 | / 2 | | | | -1 + x / 2\ / 2 \ | | / 2 1 + 21*sin (7*x)*cos(7*x) \1 + 21*sin (7*x)*cos(7*x)/*\-1 + x / | | 2 | | / 2 | / 2 | | |
|sin (7*x)*(7*x*cos(7*x) + sin(7*x)) - 3*(7*x*cos(7*x) + sin(7*x))*\2*sin (7*x) - 49*x *sin (7*x) + 98*x *cos (7*x) + 42*x*cos(7*x)*sin(7*x)/ + 3*(7*x*cos(7*x) + sin(7*x)) *sin(7*x) - 49*x *sin (7*x)*(7*x*cos(7*x) + sin(7*x)) + 7*x*sin (7*x)*(-2*cos(7*x) + 7*x*sin(7*x)) + 21*x*(7*x*cos(7*x) + sin(7*x)) *cos(7*x) + 49*x *cos (7*x)*(7*x*cos(7*x) + sin(7*x)) + 49*x *sin (7*x)*(3*sin(7*x) + 7*x*cos(7*x)) + 21*x*(-2*cos(7*x) + 7*x*sin(7*x))*(7*x*cos(7*x) + sin(7*x))*sin(7*x) + 28*x*(7*x*cos(7*x) + sin(7*x))*cos(7*x)*sin(7*x) + 49*x *(-2*cos(7*x) + 7*x*sin(7*x))*cos(7*x)*sin(7*x) \ \1 + 21*sin (7*x)*cos(7*x)/ *\-1 + x / \1 - x / *\1 + 21*sin (7*x)*cos(7*x)/ / 2 2 | 3*sin (6*x)| |3*(7*x*cos(7*x) + sin(7*x)) \\/ 1 - x \ \/ 1 - x / / | \ \1 - x / *\1 + 21*sin (7*x)*cos(7*x)/ / \ \/ 1 - x / \ cos (6*x) / \\/ 1 - x \ \/ 1 - x / / |
3*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - 72*x *sin (7*x)*|1 + -----------|*|--------------------------- + ---------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| ________ 2 | 2 | | ________ / 2\ / 2 \ | 2 cos(6*x) ________ / 2 \ / 2\ |
| / 2 1 + 21*sin (7*x)*cos(7*x) \ cos (6*x) / | / 2 \1 - x /*\1 + 21*sin (7*x)*cos(7*x)/ | 1 + 21*sin (7*x)*cos(7*x) / 2 \1 + 21*sin (7*x)*cos(7*x)/*\-1 + x / |
\ \/ 1 - x \ \/ 1 - x / \/ 1 - x *cos(6*x) /
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/ 2 \ 2
\1 + 21*sin (7*x)*cos(7*x)/*cos (6*x)
$$\frac{3 \left(- \frac{x^{3} \left(\frac{- \frac{x^{3}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{49 x^{2} \sin^{3}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2058 x \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 7203 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} - 14406 \sqrt{1 - x^{2}} \sin{\left(7 x \right)} \cos^{2}{\left(7 x \right)} + 343 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)} + 98 \left(\frac{x^{2} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{28 x \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 98 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} - 98 \sqrt{1 - x^{2}} \cos^{2}{\left(7 x \right)} + \frac{\sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right) \sin{\left(7 x \right)} - 7 \left(\frac{3 x^{3} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{42 x^{2} \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{294 x \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{294 x \cos^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{3 x \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 2744 \sqrt{1 - x^{2}} \sin{\left(7 x \right)} \cos{\left(7 x \right)} + \frac{42 \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right) \cos{\left(7 x \right)} + \frac{49 \sin^{3}{\left(7 x \right)}}{\sqrt{1 - x^{2}}}}{x^{2} - 1} + \frac{2 \left(\frac{x}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} + 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right)^{3}}{\left(x^{2} - 1\right)^{2} \left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right)^{2}} + \frac{2 \left(\frac{x}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} + 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right) \left(\frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{147 x \sin^{3}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 3087 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} - 147 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)} + 21 \left(\frac{x^{2} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{28 x \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 98 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} - 98 \sqrt{1 - x^{2}} \cos^{2}{\left(7 x \right)} + \frac{\sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right) \cos{\left(7 x \right)} + \frac{1}{\sqrt{1 - x^{2}}}\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right)}\right) \sin^{3}{\left(7 x \right)}}{21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1} - \frac{576 x^{3} \left(\frac{3 \sin^{2}{\left(6 x \right)}}{\cos^{2}{\left(6 x \right)}} + 2\right) \sin{\left(6 x \right)} \sin^{3}{\left(7 x \right)}}{\sqrt{1 - x^{2}} \cos{\left(6 x \right)}} + \frac{3 x^{2} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \left(\frac{\frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{147 x \sin^{3}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 3087 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} - 147 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)} + 21 \left(\frac{x^{2} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{28 x \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 98 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} - 98 \sqrt{1 - x^{2}} \cos^{2}{\left(7 x \right)} + \frac{\sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right) \cos{\left(7 x \right)} + \frac{1}{\sqrt{1 - x^{2}}}}{x^{2} - 1} - \frac{2 \left(\frac{x}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} + 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right)^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right)}\right) \sin^{2}{\left(7 x \right)}}{21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1} - 72 x^{2} \left(\frac{3 \sin^{2}{\left(6 x \right)}}{\cos^{2}{\left(6 x \right)}} + 1\right) \left(\frac{x \left(\frac{x}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} + 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)}}{\left(1 - x^{2}\right) \left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right)} + \frac{3 \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right)}{\sqrt{1 - x^{2}}}\right) \sin^{2}{\left(7 x \right)} + \frac{12 x \left(\frac{x^{2} \left(\frac{\frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{147 x \sin^{3}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 3087 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} - 147 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)} + 21 \left(\frac{x^{2} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{28 x \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 98 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} - 98 \sqrt{1 - x^{2}} \cos^{2}{\left(7 x \right)} + \frac{\sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right) \cos{\left(7 x \right)} + \frac{1}{\sqrt{1 - x^{2}}}}{x^{2} - 1} - \frac{2 \left(\frac{x}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} + 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right)^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right)}\right) \sin^{2}{\left(7 x \right)}}{21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1} + \frac{6 x \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \left(\frac{x}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} + 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)}}{\left(x^{2} - 1\right) \left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right)} + \frac{3 \left(7 x \left(7 x \sin{\left(7 x \right)} - 2 \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} + 7 x \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \cos{\left(7 x \right)} - 3 \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right)^{2} + \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)}\right)}{\sqrt{1 - x^{2}}}\right) \sin{\left(6 x \right)} \sin{\left(7 x \right)}}{\cos{\left(6 x \right)}} - \frac{3 x \left(\frac{x}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} + 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right) \left(7 x \left(7 x \sin{\left(7 x \right)} - 2 \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} + 7 x \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \cos{\left(7 x \right)} - 3 \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right)^{2} + \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)}}{\left(x^{2} - 1\right) \left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right)} + \frac{49 x^{2} \left(7 x \sin{\left(7 x \right)} - 2 \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)} - 49 x^{2} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)} + 49 x^{2} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \cos^{2}{\left(7 x \right)} + 49 x^{2} \left(7 x \cos{\left(7 x \right)} + 3 \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)} + 21 x \left(7 x \sin{\left(7 x \right)} - 2 \cos{\left(7 x \right)}\right) \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)} + 7 x \left(7 x \sin{\left(7 x \right)} - 2 \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)} + 21 x \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right)^{2} \cos{\left(7 x \right)} + 28 x \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)} + 3 \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right)^{2} \sin{\left(7 x \right)} - 3 \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \left(- 49 x^{2} \sin^{2}{\left(7 x \right)} + 98 x^{2} \cos^{2}{\left(7 x \right)} + 42 x \sin{\left(7 x \right)} \cos{\left(7 x \right)} + 2 \sin^{2}{\left(7 x \right)}\right) + \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right)}{\left(21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 1\right) \cos^{2}{\left(6 x \right)}}$$
Gráfico