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- 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
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- Derivada de:
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Derivada de 6/x
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Derivada de 9/x
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Derivada de e^(x/2)
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Derivada de (x-1)/(x+1)
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Expresiones idénticas
- acos(exp^(dos - tres x^ cuatro))^ cuatro ÷sqrt(cosh(2x-3))
- arco coseno de eno de ( exponente de en el grado (2 menos 3x en el grado 4)) en el grado 4÷ raíz cuadrada de ( coseno de eno hiperbólico de (2x menos 3))
- arco coseno de eno de ( exponente de en el grado (dos menos tres x en el grado cuatro)) en el grado cuatro ÷ raíz cuadrada de ( coseno de eno hiperbólico de (2x menos 3))
- acos(exp^(2-3x^4))^4÷√(cosh(2x-3))
- acos(exp(2-3x4))4÷sqrt(cosh(2x-3))
- acosexp2-3x44÷sqrtcosh2x-3
- acos(exp^(2-3x⁴))⁴÷sqrt(cosh(2x-3))
- acosexp^2-3x^4^4÷sqrtcosh2x-3
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Expresiones semejantes
- acos(exp^(2+3x^4))^4÷sqrt(cosh(2x-3))
- acos(exp^(2-3x^4))^4÷sqrt(cosh(2x+3))
- arccos(exp^(2-3x^4))^4÷sqrt(cosh(2x-3))
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Expresiones con funciones
- Arcocoseno arccos
- acos(2*t)-asin(3*t)
- acos(2*x)^(3)
- acos(t)^(3)
- acos(2*x-1)
- acos(2x)
- Exponente exp
- exp(x)/(exp(x)-1)
- exp(x)^x
- exp(sin2x)
- exp(3*x)
- exp(8*x)
- Raíz cuadrada sqrt
- sqrt(x+2)
- sqrt(x-1)/(sqrt(x^2-x)-1)
- sqrt(2*x-1)
- sqrtsinx
- sqrt(x)+3*x^3
- Coseno hiperbólico cosh
- cosh(3*x)/3
- coshx
Derivada de acos(exp^(2-3x^4))^4÷sqrt(cosh(2x-3))
Solución
Ha introducido
[src]
/ 4\
4| 2 - 3*x |
acos \E /
-----------------
_______________
\/ cosh(2*x - 3)
$$\frac{\operatorname{acos}^{4}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{\cosh{\left(2 x - 3 \right)}}}$$
acos(E^(2 - 3*x^4))^4/sqrt(cosh(2*x - 3))
Primera derivada
[src]
/ 4\ / 4\ 4
4| 2 - 3*x | 3 3| 2 - 3*x | 2 - 3*x
acos \E /*sinh(2*x - 3) 48*x *acos \E /*e
- ------------------------------ + -------------------------------------
3/2 _______________
cosh (2*x - 3) / 4
/ 4 - 6*x _______________
\/ 1 - e *\/ cosh(2*x - 3)
$$\frac{48 x^{3} e^{2 - 3 x^{4}} \operatorname{acos}^{3}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}} \sqrt{\cosh{\left(2 x - 3 \right)}}} - \frac{\sinh{\left(2 x - 3 \right)} \operatorname{acos}^{4}{\left(e^{2 - 3 x^{4}} \right)}}{\cosh^{\frac{3}{2}}{\left(2 x - 3 \right)}}$$
Segunda derivada
[src]
/ / / 4\ 4 4 / 4\ 4 / 4\ 4\ / 4\ 4 \
/ 4\ | / 4\ / 2 \ | | 2 - 3*x | 2 - 3*x 4 4 - 6*x 4 | 2 - 3*x | 6 - 9*x 4 | 2 - 3*x | 2 - 3*x | 3 | 2 - 3*x | 2 - 3*x |
2| 2 - 3*x | | 2| 2 - 3*x | | 3*sinh (-3 + 2*x)| 2 | acos\e /*e 12*x *e 4*x *acos\e /*e 4*x *acos\e /*e | 96*x *acos\e /*e *sinh(-3 + 2*x)|
acos \e /*|acos \e /*|-2 + -----------------| - 144*x *|- ------------------------- - --------------- + ------------------------------ + ------------------------------| - ----------------------------------------------|
| | 2 | | _______________ 4 3/2 _______________ | _______________ |
| \ cosh (-3 + 2*x) / | / 4 4 - 6*x / 4\ / 4 | / 4 |
| | / 4 - 6*x 1 - e | 4 - 6*x | / 4 - 6*x | / 4 - 6*x |
\ \ \/ 1 - e \1 - e / \/ 1 - e / \/ 1 - e *cosh(-3 + 2*x) /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
________________
\/ cosh(-3 + 2*x)
$$\frac{\left(- \frac{96 x^{3} e^{2 - 3 x^{4}} \sinh{\left(2 x - 3 \right)} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}} \cosh{\left(2 x - 3 \right)}} - 144 x^{2} \left(- \frac{12 x^{4} e^{4 - 6 x^{4}}}{1 - e^{4 - 6 x^{4}}} + \frac{4 x^{4} e^{2 - 3 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}} + \frac{4 x^{4} e^{6 - 9 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{3}{2}}} - \frac{e^{2 - 3 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}}\right) + \left(\frac{3 \sinh^{2}{\left(2 x - 3 \right)}}{\cosh^{2}{\left(2 x - 3 \right)}} - 2\right) \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}\right) \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{\cosh{\left(2 x - 3 \right)}}}$$
Tercera derivada
[src]
/ / / 4\ 4 4 / 4\ 4 / 4\ 4\ \
| | | 2 - 3*x | 2 - 3*x 4 4 - 6*x 4 | 2 - 3*x | 6 - 9*x 4 | 2 - 3*x | 2 - 3*x | / 4\ |
| 2 | acos\e /*e 12*x *e 4*x *acos\e /*e 4*x *acos\e /*e | | 2 - 3*x | |
| / 4\ / 2 \ / 4\ / 2 \ 4 432*x *|- ------------------------- - --------------- + ------------------------------ + ------------------------------|*acos\e /*sinh(-3 + 2*x)|
| 3| 2 - 3*x | | 15*sinh (-3 + 2*x)| 3 2| 2 - 3*x | | 3*sinh (-3 + 2*x)| 2 - 3*x | _______________ 4 3/2 _______________ | |
| / / 4\ 4 4 / 4\ 4 / 4\ 4 / 4\ 4 / 4\ 4 / 4\ 4 / 4\ 4 / 4\ 4 / 4\ 4\ acos \e /*|-14 + ------------------|*sinh(-3 + 2*x) 144*x *acos \e /*|-2 + -----------------|*e | / 4 4 - 6*x / 4\ / 4 | |
| | 2| 2 - 3*x | 2 - 3*x 8 6 - 9*x 8 | 2 - 3*x | 4 - 6*x 8 | 2 - 3*x | 8 - 12*x 4 2| 2 - 3*x | 6 - 9*x 4 2| 2 - 3*x | 2 - 3*x 8 2| 2 - 3*x | 2 - 3*x 4 | 2 - 3*x | 4 - 6*x 8 2| 2 - 3*x | 10 - 15*x 8 2| 2 - 3*x | 6 - 9*x | | 2 | | 2 | | / 4 - 6*x 1 - e | 4 - 6*x | / 4 - 6*x | | / 4\
| |acos \e /*e 144*x *e 216*x *acos\e /*e 216*x *acos\e /*e 18*x *acos \e /*e 18*x *acos \e /*e 24*x *acos \e /*e 54*x *acos\e /*e 72*x *acos \e /*e 96*x *acos \e /*e | \ cosh (-3 + 2*x) / \ cosh (-3 + 2*x) / \ \/ 1 - e \1 - e / \/ 1 - e / | | 2 - 3*x |
|288*x*|-------------------------- + ------------------ - -------------------------------- - --------------------------------- - -------------------------------- - -------------------------------- + -------------------------------- + ------------------------------- + ---------------------------------- + --------------------------------| - ---------------------------------------------------------- + ---------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------|*acos\e /
| | _______________ 3/2 4 2 3/2 _______________ _______________ 4 5/2 3/2 | cosh(-3 + 2*x) _______________ cosh(-3 + 2*x) |
| | / 4 / 4\ 4 - 6*x / 4\ / 4\ / 4 / 4 4 - 6*x / 4\ / 4\ | / 4 |
| | / 4 - 6*x | 4 - 6*x | 1 - e | 4 - 6*x | | 4 - 6*x | / 4 - 6*x / 4 - 6*x 1 - e | 4 - 6*x | | 4 - 6*x | | / 4 - 6*x |
\ \ \/ 1 - e \1 - e / \1 - e / \1 - e / \/ 1 - e \/ 1 - e \1 - e / \1 - e / / \/ 1 - e /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
________________
\/ cosh(-3 + 2*x)
$$\frac{\left(\frac{144 x^{3} \left(\frac{3 \sinh^{2}{\left(2 x - 3 \right)}}{\cosh^{2}{\left(2 x - 3 \right)}} - 2\right) e^{2 - 3 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}} + \frac{432 x^{2} \left(- \frac{12 x^{4} e^{4 - 6 x^{4}}}{1 - e^{4 - 6 x^{4}}} + \frac{4 x^{4} e^{2 - 3 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}} + \frac{4 x^{4} e^{6 - 9 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{3}{2}}} - \frac{e^{2 - 3 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}}\right) \sinh{\left(2 x - 3 \right)} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\cosh{\left(2 x - 3 \right)}} + 288 x \left(- \frac{216 x^{8} e^{4 - 6 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{1 - e^{4 - 6 x^{4}}} - \frac{216 x^{8} e^{8 - 12 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{2}} + \frac{24 x^{8} e^{2 - 3 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}} + \frac{96 x^{8} e^{6 - 9 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{3}{2}}} + \frac{144 x^{8} e^{6 - 9 x^{4}}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{3}{2}}} + \frac{72 x^{8} e^{10 - 15 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{5}{2}}} + \frac{54 x^{4} e^{4 - 6 x^{4}} \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{1 - e^{4 - 6 x^{4}}} - \frac{18 x^{4} e^{2 - 3 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}} - \frac{18 x^{4} e^{6 - 9 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\left(1 - e^{4 - 6 x^{4}}\right)^{\frac{3}{2}}} + \frac{e^{2 - 3 x^{4}} \operatorname{acos}^{2}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{1 - e^{4 - 6 x^{4}}}}\right) - \frac{\left(\frac{15 \sinh^{2}{\left(2 x - 3 \right)}}{\cosh^{2}{\left(2 x - 3 \right)}} - 14\right) \sinh{\left(2 x - 3 \right)} \operatorname{acos}^{3}{\left(e^{2 - 3 x^{4}} \right)}}{\cosh{\left(2 x - 3 \right)}}\right) \operatorname{acos}{\left(e^{2 - 3 x^{4}} \right)}}{\sqrt{\cosh{\left(2 x - 3 \right)}}}$$
Gráfico