Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de 1/t
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de f(x)=√x
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Expresiones idénticas
- y=sqrt(arccos(3x))*sin^52x
- y es igual a raíz cuadrada de (arc coseno de (3x)) multiplicar por seno de en el grado 52x
- y=√(arccos(3x))*sin^52x
- y=sqrt(arccos(3x))*sin52x
- y=sqrtarccos3x*sin52x
- y=sqrt(arccos(3x))*sin⁵2x
- y=sqrt(arccos(3x))sin^52x
- y=sqrt(arccos(3x))sin52x
- y=sqrtarccos3xsin52x
- y=sqrtarccos3xsin^52x
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x^4+2x)
- sqrt(x)*asin(sqrt(x))+sqrt(1-x)
- sqrt(x)/2
- sqrt(x-1)/(sqrt(x)*2-x-1)
- sqrt(x^4-3*x)
- Seno sin
- sin(x)cos(x)
- sin(t)*cos(t)
- sin(3*x^2)/((3*x^2))
- sin(3*x-pi/12)
- sin(5*x+2)
Derivada de y=sqrt(arccos(3x))*sin^52x
Solución
Ha introducido
[src]
___________ 5 \/ acos(3*x) *sin (2*x)
$$\sin^{5}{\left(2 x \right)} \sqrt{\operatorname{acos}{\left(3 x \right)}}$$
sqrt(acos(3*x))*sin(2*x)^5
Primera derivada
[src]
5
___________ 4 3*sin (2*x)
10*\/ acos(3*x) *sin (2*x)*cos(2*x) - -----------------------------
__________
/ 2 ___________
2*\/ 1 - 9*x *\/ acos(3*x)
$$10 \sin^{4}{\left(2 x \right)} \cos{\left(2 x \right)} \sqrt{\operatorname{acos}{\left(3 x \right)}} - \frac{3 \sin^{5}{\left(2 x \right)}}{2 \sqrt{1 - 9 x^{2}} \sqrt{\operatorname{acos}{\left(3 x \right)}}}$$
Segunda derivada
[src]
/ 2 / 1 6*x \ \
| 9*sin (2*x)*|- --------------------- + -------------| |
| | / 2\ 3/2| |
| | \-1 + 9*x /*acos(3*x) / 2\ | |
3 | ___________ / 2 2 \ \ \1 - 9*x / / 30*cos(2*x)*sin(2*x) |
-sin (2*x)*|20*\/ acos(3*x) *\sin (2*x) - 4*cos (2*x)/ + ----------------------------------------------------- + ---------------------------|
| ___________ __________ |
| 4*\/ acos(3*x) / 2 ___________|
\ \/ 1 - 9*x *\/ acos(3*x) /
$$- \left(\frac{9 \left(\frac{6 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{\left(9 x^{2} - 1\right) \operatorname{acos}{\left(3 x \right)}}\right) \sin^{2}{\left(2 x \right)}}{4 \sqrt{\operatorname{acos}{\left(3 x \right)}}} + 20 \left(\sin^{2}{\left(2 x \right)} - 4 \cos^{2}{\left(2 x \right)}\right) \sqrt{\operatorname{acos}{\left(3 x \right)}} + \frac{30 \sin{\left(2 x \right)} \cos{\left(2 x \right)}}{\sqrt{1 - 9 x^{2}} \sqrt{\operatorname{acos}{\left(3 x \right)}}}\right) \sin^{3}{\left(2 x \right)}$$
Tercera derivada
[src]
/ / 2 \ \
| 3 | 4 3 108*x 18*x | 2 / 1 6*x \ |
| 27*sin (2*x)*|------------- + ------------------------ + ------------- + ----------------------| 135*sin (2*x)*|- --------------------- + -------------|*cos(2*x)|
| | 3/2 3/2 5/2 2 | | / 2\ 3/2| |
| |/ 2\ / 2\ 2 / 2\ / 2\ | / 2 2 \ | \-1 + 9*x /*acos(3*x) / 2\ | |
2 | ___________ / 2 2 \ \\1 - 9*x / \1 - 9*x / *acos (3*x) \1 - 9*x / \-1 + 9*x / *acos(3*x)/ 90*\sin (2*x) - 4*cos (2*x)/*sin(2*x) \ \1 - 9*x / / |
sin (2*x)*|- 40*\/ acos(3*x) *\- 12*cos (2*x) + 13*sin (2*x)/*cos(2*x) - ------------------------------------------------------------------------------------------------ + ------------------------------------- - ----------------------------------------------------------------|
| ___________ __________ ___________ |
| 8*\/ acos(3*x) / 2 ___________ 2*\/ acos(3*x) |
\ \/ 1 - 9*x *\/ acos(3*x) /
$$\left(- \frac{135 \left(\frac{6 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{\left(9 x^{2} - 1\right) \operatorname{acos}{\left(3 x \right)}}\right) \sin^{2}{\left(2 x \right)} \cos{\left(2 x \right)}}{2 \sqrt{\operatorname{acos}{\left(3 x \right)}}} - 40 \left(13 \sin^{2}{\left(2 x \right)} - 12 \cos^{2}{\left(2 x \right)}\right) \cos{\left(2 x \right)} \sqrt{\operatorname{acos}{\left(3 x \right)}} - \frac{27 \left(\frac{108 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} + \frac{18 x}{\left(9 x^{2} - 1\right)^{2} \operatorname{acos}{\left(3 x \right)}} + \frac{4}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(3 x \right)}}\right) \sin^{3}{\left(2 x \right)}}{8 \sqrt{\operatorname{acos}{\left(3 x \right)}}} + \frac{90 \left(\sin^{2}{\left(2 x \right)} - 4 \cos^{2}{\left(2 x \right)}\right) \sin{\left(2 x \right)}}{\sqrt{1 - 9 x^{2}} \sqrt{\operatorname{acos}{\left(3 x \right)}}}\right) \sin^{2}{\left(2 x \right)}$$
Gráfico