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/(x+3)
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Derivada de 4*y
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Derivada de (2x-7)^8
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Derivada de (-1)/x-3*x
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Expresiones idénticas
- y=(siete ^cos4x)*(arctg^ tres)(5x)
- y es igual a (7 en el grado coseno de 4x) multiplicar por (arctg al cubo )(5x)
- y es igual a (siete en el grado coseno de 4x) multiplicar por (arctg en el grado tres)(5x)
- y=(7cos4x)*(arctg3)(5x)
- y=7cos4x*arctg35x
- y=(7^cos4x)*(arctg³)(5x)
- y=(7 en el grado cos4x)*(arctg en el grado 3)(5x)
- y=(7^cos4x)(arctg^3)(5x)
- y=(7cos4x)(arctg3)(5x)
- y=7cos4xarctg35x
- y=7^cos4xarctg^35x
Derivada de y=(7^cos4x)*(arctg^3)(5x)
Solución
Ha introducido
[src]
cos(4*x) 3 7 *atan (x)*5*x
$$5 x 7^{\cos{\left(4 x \right)}} \operatorname{atan}^{3}{\left(x \right)}$$
(7^cos(4*x)*atan(x)^3)*(5*x)
Primera derivada
[src]
/ cos(4*x) 2 \
|3*7 *atan (x) cos(4*x) 3 | cos(4*x) 3
5*x*|-------------------- - 4*7 *atan (x)*log(7)*sin(4*x)| + 5*7 *atan (x)
| 2 |
\ 1 + x /
$$5 \cdot 7^{\cos{\left(4 x \right)}} \operatorname{atan}^{3}{\left(x \right)} + 5 x \left(- 4 \cdot 7^{\cos{\left(4 x \right)}} \log{\left(7 \right)} \sin{\left(4 x \right)} \operatorname{atan}^{3}{\left(x \right)} + \frac{3 \cdot 7^{\cos{\left(4 x \right)}} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1}\right)$$
Segunda derivada
[src]
cos(4*x) / /3*(-1 + x*atan(x)) 2 / 2 \ 12*atan(x)*log(7)*sin(4*x)\ 3*atan(x) 2 \
10*7 *|- x*|------------------ - 8*atan (x)*\-cos(4*x) + sin (4*x)*log(7)/*log(7) + --------------------------| + --------- - 4*atan (x)*log(7)*sin(4*x)|*atan(x)
| | 2 2 | 2 |
| | / 2\ 1 + x | 1 + x |
\ \ \1 + x / / /
$$10 \cdot 7^{\cos{\left(4 x \right)}} \left(- x \left(- 8 \left(\log{\left(7 \right)} \sin^{2}{\left(4 x \right)} - \cos{\left(4 x \right)}\right) \log{\left(7 \right)} \operatorname{atan}^{2}{\left(x \right)} + \frac{12 \log{\left(7 \right)} \sin{\left(4 x \right)} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 \left(x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}}\right) - 4 \log{\left(7 \right)} \sin{\left(4 x \right)} \operatorname{atan}^{2}{\left(x \right)} + \frac{3 \operatorname{atan}{\left(x \right)}}{x^{2} + 1}\right) \operatorname{atan}{\left(x \right)}$$
Tercera derivada
[src]
/ / / 2 2 \ \ \
| | | 1 2 6*x*atan(x) 4*x *atan (x)| | |
| |3*|------ - atan (x) - ----------- + -------------| | |
| | | 2 2 2 | 2 / 2 \ | |
cos(4*x) | | \1 + x 1 + x 1 + x / 3 / 2 2 \ 72*atan (x)*\-cos(4*x) + sin (4*x)*log(7)/*log(7) 36*(-1 + x*atan(x))*atan(x)*log(7)*sin(4*x)| /3*(-1 + x*atan(x)) 2 / 2 \ 12*atan(x)*log(7)*sin(4*x)\ |
10*7 *|x*|--------------------------------------------------- + 32*atan (x)*\1 - log (7)*sin (4*x) + 3*cos(4*x)*log(7)/*log(7)*sin(4*x) + ------------------------------------------------- + -------------------------------------------| - 3*|------------------ - 8*atan (x)*\-cos(4*x) + sin (4*x)*log(7)/*log(7) + --------------------------|*atan(x)|
| | 2 2 2 | | 2 2 | |
| | / 2\ 1 + x / 2\ | | / 2\ 1 + x | |
\ \ \1 + x / \1 + x / / \ \1 + x / / /
$$10 \cdot 7^{\cos{\left(4 x \right)}} \left(x \left(32 \left(- \log{\left(7 \right)}^{2} \sin^{2}{\left(4 x \right)} + 3 \log{\left(7 \right)} \cos{\left(4 x \right)} + 1\right) \log{\left(7 \right)} \sin{\left(4 x \right)} \operatorname{atan}^{3}{\left(x \right)} + \frac{72 \left(\log{\left(7 \right)} \sin^{2}{\left(4 x \right)} - \cos{\left(4 x \right)}\right) \log{\left(7 \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{36 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \log{\left(7 \right)} \sin{\left(4 x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{1}{x^{2} + 1}\right)}{\left(x^{2} + 1\right)^{2}}\right) - 3 \left(- 8 \left(\log{\left(7 \right)} \sin^{2}{\left(4 x \right)} - \cos{\left(4 x \right)}\right) \log{\left(7 \right)} \operatorname{atan}^{2}{\left(x \right)} + \frac{12 \log{\left(7 \right)} \sin{\left(4 x \right)} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 \left(x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}}\right) \operatorname{atan}{\left(x \right)}\right)$$
Gráfico