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 x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Derivada de (t^(2)+1)÷(t^(1÷2)-1)
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Expresiones idénticas
- y=arctg^34x3^sinx
- y es igual a arctg al cubo 4x3 en el grado seno de x
- y=arctg34x3sinx
- y=arctg³4x3^sinx
- y=arctg en el grado 34x3 en el grado sinx
Derivada de y=arctg^34x3^sinx
Solución
Ha introducido
[src]
3 sin(x) atan (4*x)*3
$$3^{\sin{\left(x \right)}} \operatorname{atan}^{3}{\left(4 x \right)}$$
atan(4*x)^3*3^sin(x)
Primera derivada
[src]
sin(x) 2
12*3 *atan (4*x) sin(x) 3
--------------------- + 3 *atan (4*x)*cos(x)*log(3)
2
1 + 16*x
$$3^{\sin{\left(x \right)}} \log{\left(3 \right)} \cos{\left(x \right)} \operatorname{atan}^{3}{\left(4 x \right)} + \frac{12 \cdot 3^{\sin{\left(x \right)}} \operatorname{atan}^{2}{\left(4 x \right)}}{16 x^{2} + 1}$$
Segunda derivada
[src]
sin(x) / 96*(-1 + 4*x*atan(4*x)) 2 / 2 \ 24*atan(4*x)*cos(x)*log(3)\
3 *|- ----------------------- - atan (4*x)*\- cos (x)*log(3) + sin(x)/*log(3) + --------------------------|*atan(4*x)
| 2 2 |
| / 2\ 1 + 16*x |
\ \1 + 16*x / /
$$3^{\sin{\left(x \right)}} \left(- \left(\sin{\left(x \right)} - \log{\left(3 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(3 \right)} \operatorname{atan}^{2}{\left(4 x \right)} + \frac{24 \log{\left(3 \right)} \cos{\left(x \right)} \operatorname{atan}{\left(4 x \right)}}{16 x^{2} + 1} - \frac{96 \left(4 x \operatorname{atan}{\left(4 x \right)} - 1\right)}{\left(16 x^{2} + 1\right)^{2}}\right) \operatorname{atan}{\left(4 x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \
| | 1 2 24*x*atan(4*x) 64*x *atan (4*x)| |
|384*|--------- - atan (4*x) - -------------- + ----------------| |
| | 2 2 2 | 2 / 2 \ |
sin(x) | \1 + 16*x 1 + 16*x 1 + 16*x / 3 / 2 2 \ 36*atan (4*x)*\- cos (x)*log(3) + sin(x)/*log(3) 288*(-1 + 4*x*atan(4*x))*atan(4*x)*cos(x)*log(3)|
3 *|---------------------------------------------------------------- - atan (4*x)*\1 - cos (x)*log (3) + 3*log(3)*sin(x)/*cos(x)*log(3) - ------------------------------------------------ - ------------------------------------------------|
| 2 2 2 |
| / 2\ 1 + 16*x / 2\ |
\ \1 + 16*x / \1 + 16*x / /
$$3^{\sin{\left(x \right)}} \left(- \left(3 \log{\left(3 \right)} \sin{\left(x \right)} - \log{\left(3 \right)}^{2} \cos^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)} \cos{\left(x \right)} \operatorname{atan}^{3}{\left(4 x \right)} - \frac{36 \left(\sin{\left(x \right)} - \log{\left(3 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(3 \right)} \operatorname{atan}^{2}{\left(4 x \right)}}{16 x^{2} + 1} - \frac{288 \left(4 x \operatorname{atan}{\left(4 x \right)} - 1\right) \log{\left(3 \right)} \cos{\left(x \right)} \operatorname{atan}{\left(4 x \right)}}{\left(16 x^{2} + 1\right)^{2}} + \frac{384 \left(\frac{64 x^{2} \operatorname{atan}^{2}{\left(4 x \right)}}{16 x^{2} + 1} - \frac{24 x \operatorname{atan}{\left(4 x \right)}}{16 x^{2} + 1} - \operatorname{atan}^{2}{\left(4 x \right)} + \frac{1}{16 x^{2} + 1}\right)}{\left(16 x^{2} + 1\right)^{2}}\right)$$
Gráfico