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+1)^2
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Derivada de x^(2/3)
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Derivada de 3^x
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Derivada de e^x^2
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Expresiones idénticas
- y=arctg^5x*log2(x- tres)
- y es igual a arctg en el grado 5x multiplicar por logaritmo de 2(x menos 3)
- y es igual a arctg en el grado 5x multiplicar por logaritmo de 2(x menos tres)
- y=arctg5x*log2(x-3)
- y=arctg5x*log2x-3
- y=arctg⁵x*log2(x-3)
- y=arctg^5xlog2(x-3)
- y=arctg5xlog2(x-3)
- y=arctg5xlog2x-3
- y=arctg^5xlog2x-3
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Expresiones semejantes
- y=arctg^5x*log2(x+3)
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Expresiones con funciones
- arctg
- arctgx
- arctg(x^1/2)
- arctg(x^2-4x)
- arctgx^2
- arctg(1/x)
Derivada de y=arctg^5x*log2(x-3)
Solución
Ha introducido
[src]
5 log(x - 3)
atan (x)*----------
log(2)
$$\frac{\log{\left(x - 3 \right)}}{\log{\left(2 \right)}} \operatorname{atan}^{5}{\left(x \right)}$$
atan(x)^5*(log(x - 3)/log(2))
Primera derivada
[src]
5 4
atan (x) 5*atan (x)*log(x - 3)
-------------- + ---------------------
(x - 3)*log(2) / 2\
\1 + x /*log(2)
$$\frac{5 \log{\left(x - 3 \right)} \operatorname{atan}^{4}{\left(x \right)}}{\left(x^{2} + 1\right) \log{\left(2 \right)}} + \frac{\operatorname{atan}^{5}{\left(x \right)}}{\left(x - 3\right) \log{\left(2 \right)}}$$
Segunda derivada
[src]
/ 2 \
3 | atan (x) 10*(-2 + x*atan(x))*log(-3 + x) 10*atan(x) |
atan (x)*|- --------- - ------------------------------- + -----------------|
| 2 2 / 2\ |
| (-3 + x) / 2\ \1 + x /*(-3 + x)|
\ \1 + x / /
----------------------------------------------------------------------------
log(2)
$$\frac{\left(- \frac{10 \left(x \operatorname{atan}{\left(x \right)} - 2\right) \log{\left(x - 3 \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{10 \operatorname{atan}{\left(x \right)}}{\left(x - 3\right) \left(x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{\left(x - 3\right)^{2}}\right) \operatorname{atan}^{3}{\left(x \right)}}{\log{\left(2 \right)}}$$
Tercera derivada
[src]
/ / 2 2 \ \
| | 2 6 12*x*atan(x) 4*x *atan (x)| |
| 10*|- atan (x) + ------ - ------------ + -------------|*log(-3 + x) |
| 3 2 | 2 2 2 | |
2 |2*atan (x) 15*atan (x) \ 1 + x 1 + x 1 + x / 30*(-2 + x*atan(x))*atan(x)|
atan (x)*|---------- - ------------------ + ------------------------------------------------------------------- - ---------------------------|
| 3 / 2\ 2 2 2 |
|(-3 + x) \1 + x /*(-3 + x) / 2\ / 2\ |
\ \1 + x / \1 + x / *(-3 + x) /
----------------------------------------------------------------------------------------------------------------------------------------------
log(2)
$$\frac{\left(\frac{10 \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{12 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{6}{x^{2} + 1}\right) \log{\left(x - 3 \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{30 \left(x \operatorname{atan}{\left(x \right)} - 2\right) \operatorname{atan}{\left(x \right)}}{\left(x - 3\right) \left(x^{2} + 1\right)^{2}} - \frac{15 \operatorname{atan}^{2}{\left(x \right)}}{\left(x - 3\right)^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{atan}^{3}{\left(x \right)}}{\left(x - 3\right)^{3}}\right) \operatorname{atan}^{2}{\left(x \right)}}{\log{\left(2 \right)}}$$
Gráfico