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:
-
Derivada de x^3+(50-x)^3
- Derivada de x^2/a^2
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Derivada de x^(-2/7)
- Derivada de √x(2x-4)
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Expresiones idénticas
- y=(arctg(sqrt(x)))^ln(x)
- y es igual a (arctg( raíz cuadrada de (x))) en el grado ln(x)
- y=(arctg(√(x)))^ln(x)
- y=(arctg(sqrt(x)))ln(x)
- y=arctgsqrtxlnx
- y=arctgsqrtx^lnx
Derivada de y=(arctg(sqrt(x)))^ln(x)
Solución
Ha introducido
[src]
log(x)/ ___\ atan \\/ x /
$$\operatorname{atan}^{\log{\left(x \right)}}{\left(\sqrt{x} \right)}$$
atan(sqrt(x))^log(x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ / / ___\\ \
log(x)/ ___\ |log\atan\\/ x // log(x) |
atan \\/ x /*|---------------- + ---------------------------|
| x ___ / ___\|
\ 2*\/ x *(1 + x)*atan\\/ x //
$$\left(\frac{\log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{x} + \frac{\log{\left(x \right)}}{2 \sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(\sqrt{x} \right)}$$
Segunda derivada
[src]
/ 2 \
|/ / / ___\\ \ |
||2*log\atan\\/ x // log(x) | |
||------------------ + -------------------------| |
|| x ___ / ___\| / / ___\\ |
log(x)/ ___\ |\ \/ x *(1 + x)*atan\\/ x // log\atan\\/ x // 1 log(x) log(x) log(x) |
atan \\/ x /*|------------------------------------------------- - ---------------- + ------------------------ - ---------------------------- - ------------------------- - --------------------------|
| 4 2 3/2 / ___\ ___ 2 / ___\ 2 2/ ___\ 3/2 / ___\|
\ x x *(1 + x)*atan\\/ x / 2*\/ x *(1 + x) *atan\\/ x / 4*x*(1 + x) *atan \\/ x / 4*x *(1 + x)*atan\\/ x //
$$\left(\frac{\left(\frac{2 \log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{x} + \frac{\log{\left(x \right)}}{\sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right)^{2}}{4} - \frac{\log{\left(x \right)}}{4 x \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} - \frac{\log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{x^{2}} - \frac{\log{\left(x \right)}}{2 \sqrt{x} \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} - \frac{\log{\left(x \right)}}{4 x^{\frac{3}{2}} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{1}{x^{\frac{3}{2}} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(\sqrt{x} \right)}$$
Tercera derivada
[src]
/ 3 \
|/ / / ___\\ \ / / / ___\\ \ / / / ___\\ \ |
||2*log\atan\\/ x // log(x) | |2*log\atan\\/ x // log(x) | |4*log\atan\\/ x // 4 log(x) log(x) 2*log(x) | |
||------------------ + -------------------------| 3*|------------------ + -------------------------|*|------------------ - ------------------------ + ----------------------- + ------------------------ + --------------------------| |
|| x ___ / ___\| / / ___\\ | x ___ / ___\| | 2 3/2 / ___\ 2 2/ ___\ 3/2 / ___\ ___ 2 / ___\| |
log(x)/ ___\ |\ \/ x *(1 + x)*atan\\/ x // 2*log\atan\\/ x // \ \/ x *(1 + x)*atan\\/ x // \ x x *(1 + x)*atan\\/ x / x*(1 + x) *atan \\/ x / x *(1 + x)*atan\\/ x / \/ x *(1 + x) *atan\\/ x // 9 3 3 log(x) log(x) log(x) 3*log(x) 3*log(x) 3*log(x) |
atan \\/ x /*|------------------------------------------------- + ------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -------------------------- - --------------------------- - -------------------------- + -------------------------- + --------------------------- + ---------------------------- + ------------------------- + -------------------------- + --------------------------|
| 8 3 8 5/2 / ___\ 3/2 2 / ___\ 2 2 2/ ___\ ___ 3 / ___\ 3/2 2 / ___\ 3/2 3 3/ ___\ 3 2/ ___\ 2 2 2/ ___\ 5/2 / ___\|
\ x 4*x *(1 + x)*atan\\/ x / 2*x *(1 + x) *atan\\/ x / 4*x *(1 + x) *atan \\/ x / \/ x *(1 + x) *atan\\/ x / 2*x *(1 + x) *atan\\/ x / 4*x *(1 + x) *atan \\/ x / 4*x*(1 + x) *atan \\/ x / 8*x *(1 + x) *atan \\/ x / 8*x *(1 + x)*atan\\/ x //
$$\left(\frac{\left(\frac{2 \log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{x} + \frac{\log{\left(x \right)}}{\sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right)^{3}}{8} - \frac{3 \left(\frac{2 \log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{x} + \frac{\log{\left(x \right)}}{\sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right) \left(\frac{\log{\left(x \right)}}{x \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} + \frac{4 \log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{x^{2}} + \frac{2 \log{\left(x \right)}}{\sqrt{x} \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{\log{\left(x \right)}}{x^{\frac{3}{2}} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} - \frac{4}{x^{\frac{3}{2}} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right)}{8} + \frac{3 \log{\left(x \right)}}{4 x \left(x + 1\right)^{3} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} + \frac{3 \log{\left(x \right)}}{8 x^{2} \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} - \frac{3}{4 x^{2} \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} + \frac{2 \log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{\log{\left(x \right)}}{\sqrt{x} \left(x + 1\right)^{3} \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{\log{\left(x \right)}}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} - \frac{3}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{\log{\left(x \right)}}{4 x^{\frac{3}{2}} \left(x + 1\right)^{3} \operatorname{atan}^{3}{\left(\sqrt{x} \right)}} + \frac{3 \log{\left(x \right)}}{8 x^{\frac{5}{2}} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} - \frac{9}{4 x^{\frac{5}{2}} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(\sqrt{x} \right)}$$
Gráfico