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=(lgx- cuatro)^arctg5x
- y es igual a (lgx menos 4) en el grado arctg5x
- y es igual a (lgx menos cuatro) en el grado arctg5x
- y=(lgx-4)arctg5x
- y=lgx-4arctg5x
- y=lgx-4^arctg5x
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Expresiones semejantes
- y=(lgx+4)^arctg5x
Derivada de y=(lgx-4)^arctg5x
Solución
Ha introducido
[src]
atan(5*x) (log(x) - 4)
$$\left(\log{\left(x \right)} - 4\right)^{\operatorname{atan}{\left(5 x \right)}}$$
(log(x) - 4)^atan(5*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
atan(5*x) /5*log(log(x) - 4) atan(5*x) \
(log(x) - 4) *|----------------- + --------------|
| 2 x*(log(x) - 4)|
\ 1 + 25*x /
$$\left(\frac{5 \log{\left(\log{\left(x \right)} - 4 \right)}}{25 x^{2} + 1} + \frac{\operatorname{atan}{\left(5 x \right)}}{x \left(\log{\left(x \right)} - 4\right)}\right) \left(\log{\left(x \right)} - 4\right)^{\operatorname{atan}{\left(5 x \right)}}$$
Segunda derivada
[src]
/ 2 \
atan(5*x) |/5*log(-4 + log(x)) atan(5*x) \ atan(5*x) atan(5*x) 250*x*log(-4 + log(x)) 10 |
(-4 + log(x)) *||------------------ + ---------------| - ---------------- - ----------------- - ---------------------- + ---------------------------|
|| 2 x*(-4 + log(x))| 2 2 2 2 / 2\ |
|\ 1 + 25*x / x *(-4 + log(x)) x *(-4 + log(x)) / 2\ x*\1 + 25*x /*(-4 + log(x))|
\ \1 + 25*x / /
$$\left(\log{\left(x \right)} - 4\right)^{\operatorname{atan}{\left(5 x \right)}} \left(- \frac{250 x \log{\left(\log{\left(x \right)} - 4 \right)}}{\left(25 x^{2} + 1\right)^{2}} + \left(\frac{5 \log{\left(\log{\left(x \right)} - 4 \right)}}{25 x^{2} + 1} + \frac{\operatorname{atan}{\left(5 x \right)}}{x \left(\log{\left(x \right)} - 4\right)}\right)^{2} + \frac{10}{x \left(25 x^{2} + 1\right) \left(\log{\left(x \right)} - 4\right)} - \frac{\operatorname{atan}{\left(5 x \right)}}{x^{2} \left(\log{\left(x \right)} - 4\right)} - \frac{\operatorname{atan}{\left(5 x \right)}}{x^{2} \left(\log{\left(x \right)} - 4\right)^{2}}\right)$$
3-я производная
[src]
/ 3 2 \
atan(5*x) |/5*log(-4 + log(x)) atan(5*x) \ 750 250*log(-4 + log(x)) /5*log(-4 + log(x)) atan(5*x) \ / atan(5*x) atan(5*x) 10 250*x*log(-4 + log(x))\ 15 15 2*atan(5*x) 2*atan(5*x) 3*atan(5*x) 25000*x *log(-4 + log(x))|
(-4 + log(x)) *||------------------ + ---------------| - -------------------------- - -------------------- - 3*|------------------ + ---------------|*|---------------- + ----------------- - --------------------------- + ----------------------| - ---------------------------- - ----------------------------- + ---------------- + ----------------- + ----------------- + -------------------------|
|| 2 x*(-4 + log(x))| 2 2 | 2 x*(-4 + log(x))| | 2 2 2 / 2\ 2 | 2 / 2\ 2 / 2\ 2 3 3 3 3 2 3 |
|\ 1 + 25*x / / 2\ / 2\ \ 1 + 25*x / |x *(-4 + log(x)) x *(-4 + log(x)) x*\1 + 25*x /*(-4 + log(x)) / 2\ | x *\1 + 25*x /*(-4 + log(x)) x *\1 + 25*x /*(-4 + log(x)) x *(-4 + log(x)) x *(-4 + log(x)) x *(-4 + log(x)) / 2\ |
\ \1 + 25*x / *(-4 + log(x)) \1 + 25*x / \ \1 + 25*x / / \1 + 25*x / /
$$\left(\log{\left(x \right)} - 4\right)^{\operatorname{atan}{\left(5 x \right)}} \left(\frac{25000 x^{2} \log{\left(\log{\left(x \right)} - 4 \right)}}{\left(25 x^{2} + 1\right)^{3}} + \left(\frac{5 \log{\left(\log{\left(x \right)} - 4 \right)}}{25 x^{2} + 1} + \frac{\operatorname{atan}{\left(5 x \right)}}{x \left(\log{\left(x \right)} - 4\right)}\right)^{3} - 3 \left(\frac{5 \log{\left(\log{\left(x \right)} - 4 \right)}}{25 x^{2} + 1} + \frac{\operatorname{atan}{\left(5 x \right)}}{x \left(\log{\left(x \right)} - 4\right)}\right) \left(\frac{250 x \log{\left(\log{\left(x \right)} - 4 \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{10}{x \left(25 x^{2} + 1\right) \left(\log{\left(x \right)} - 4\right)} + \frac{\operatorname{atan}{\left(5 x \right)}}{x^{2} \left(\log{\left(x \right)} - 4\right)} + \frac{\operatorname{atan}{\left(5 x \right)}}{x^{2} \left(\log{\left(x \right)} - 4\right)^{2}}\right) - \frac{250 \log{\left(\log{\left(x \right)} - 4 \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{750}{\left(25 x^{2} + 1\right)^{2} \left(\log{\left(x \right)} - 4\right)} - \frac{15}{x^{2} \left(25 x^{2} + 1\right) \left(\log{\left(x \right)} - 4\right)} - \frac{15}{x^{2} \left(25 x^{2} + 1\right) \left(\log{\left(x \right)} - 4\right)^{2}} + \frac{2 \operatorname{atan}{\left(5 x \right)}}{x^{3} \left(\log{\left(x \right)} - 4\right)} + \frac{3 \operatorname{atan}{\left(5 x \right)}}{x^{3} \left(\log{\left(x \right)} - 4\right)^{2}} + \frac{2 \operatorname{atan}{\left(5 x \right)}}{x^{3} \left(\log{\left(x \right)} - 4\right)^{3}}\right)$$
Tercera derivada
[src]
/ 3 2 \
atan(5*x) |/5*log(-4 + log(x)) atan(5*x) \ 750 250*log(-4 + log(x)) /5*log(-4 + log(x)) atan(5*x) \ / atan(5*x) atan(5*x) 10 250*x*log(-4 + log(x))\ 15 15 2*atan(5*x) 2*atan(5*x) 3*atan(5*x) 25000*x *log(-4 + log(x))|
(-4 + log(x)) *||------------------ + ---------------| - -------------------------- - -------------------- - 3*|------------------ + ---------------|*|---------------- + ----------------- - --------------------------- + ----------------------| - ---------------------------- - ----------------------------- + ---------------- + ----------------- + ----------------- + -------------------------|
|| 2 x*(-4 + log(x))| 2 2 | 2 x*(-4 + log(x))| | 2 2 2 / 2\ 2 | 2 / 2\ 2 / 2\ 2 3 3 3 3 2 3 |
|\ 1 + 25*x / / 2\ / 2\ \ 1 + 25*x / |x *(-4 + log(x)) x *(-4 + log(x)) x*\1 + 25*x /*(-4 + log(x)) / 2\ | x *\1 + 25*x /*(-4 + log(x)) x *\1 + 25*x /*(-4 + log(x)) x *(-4 + log(x)) x *(-4 + log(x)) x *(-4 + log(x)) / 2\ |
\ \1 + 25*x / *(-4 + log(x)) \1 + 25*x / \ \1 + 25*x / / \1 + 25*x / /
$$\left(\log{\left(x \right)} - 4\right)^{\operatorname{atan}{\left(5 x \right)}} \left(\frac{25000 x^{2} \log{\left(\log{\left(x \right)} - 4 \right)}}{\left(25 x^{2} + 1\right)^{3}} + \left(\frac{5 \log{\left(\log{\left(x \right)} - 4 \right)}}{25 x^{2} + 1} + \frac{\operatorname{atan}{\left(5 x \right)}}{x \left(\log{\left(x \right)} - 4\right)}\right)^{3} - 3 \left(\frac{5 \log{\left(\log{\left(x \right)} - 4 \right)}}{25 x^{2} + 1} + \frac{\operatorname{atan}{\left(5 x \right)}}{x \left(\log{\left(x \right)} - 4\right)}\right) \left(\frac{250 x \log{\left(\log{\left(x \right)} - 4 \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{10}{x \left(25 x^{2} + 1\right) \left(\log{\left(x \right)} - 4\right)} + \frac{\operatorname{atan}{\left(5 x \right)}}{x^{2} \left(\log{\left(x \right)} - 4\right)} + \frac{\operatorname{atan}{\left(5 x \right)}}{x^{2} \left(\log{\left(x \right)} - 4\right)^{2}}\right) - \frac{250 \log{\left(\log{\left(x \right)} - 4 \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{750}{\left(25 x^{2} + 1\right)^{2} \left(\log{\left(x \right)} - 4\right)} - \frac{15}{x^{2} \left(25 x^{2} + 1\right) \left(\log{\left(x \right)} - 4\right)} - \frac{15}{x^{2} \left(25 x^{2} + 1\right) \left(\log{\left(x \right)} - 4\right)^{2}} + \frac{2 \operatorname{atan}{\left(5 x \right)}}{x^{3} \left(\log{\left(x \right)} - 4\right)} + \frac{3 \operatorname{atan}{\left(5 x \right)}}{x^{3} \left(\log{\left(x \right)} - 4\right)^{2}} + \frac{2 \operatorname{atan}{\left(5 x \right)}}{x^{3} \left(\log{\left(x \right)} - 4\right)^{3}}\right)$$
Gráfico