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=(lg(7x- cinco))^arctg5x
- y es igual a (lg(7x menos 5)) en el grado arctg5x
- y es igual a (lg(7x menos cinco)) en el grado arctg5x
- y=(lg(7x-5))arctg5x
- y=lg7x-5arctg5x
- y=lg7x-5^arctg5x
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Expresiones semejantes
- y=(lg(7x+5))^arctg5x
Derivada de y=(lg(7x-5))^arctg5x
Solución
Ha introducido
[src]
atan(5*x) log (7*x - 5)
$$\log{\left(7 x - 5 \right)}^{\operatorname{atan}{\left(5 x \right)}}$$
log(7*x - 5)^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(7*x - 5)) 7*atan(5*x) \
log (7*x - 5)*|------------------- + ----------------------|
| 2 (7*x - 5)*log(7*x - 5)|
\ 1 + 25*x /
$$\left(\frac{5 \log{\left(\log{\left(7 x - 5 \right)} \right)}}{25 x^{2} + 1} + \frac{7 \operatorname{atan}{\left(5 x \right)}}{\left(7 x - 5\right) \log{\left(7 x - 5 \right)}}\right) \log{\left(7 x - 5 \right)}^{\operatorname{atan}{\left(5 x \right)}}$$
Segunda derivada
[src]
/ 2 \
atan(5*x) |/5*log(log(-5 + 7*x)) 7*atan(5*x) \ 250*x*log(log(-5 + 7*x)) 49*atan(5*x) 49*atan(5*x) 70 |
log (-5 + 7*x)*||-------------------- + ------------------------| - ------------------------ - ------------------------- - -------------------------- + ------------------------------------|
|| 2 (-5 + 7*x)*log(-5 + 7*x)| 2 2 2 2 / 2\ |
|\ 1 + 25*x / / 2\ (-5 + 7*x) *log(-5 + 7*x) (-5 + 7*x) *log (-5 + 7*x) \1 + 25*x /*(-5 + 7*x)*log(-5 + 7*x)|
\ \1 + 25*x / /
$$\left(- \frac{250 x \log{\left(\log{\left(7 x - 5 \right)} \right)}}{\left(25 x^{2} + 1\right)^{2}} + \left(\frac{5 \log{\left(\log{\left(7 x - 5 \right)} \right)}}{25 x^{2} + 1} + \frac{7 \operatorname{atan}{\left(5 x \right)}}{\left(7 x - 5\right) \log{\left(7 x - 5 \right)}}\right)^{2} + \frac{70}{\left(7 x - 5\right) \left(25 x^{2} + 1\right) \log{\left(7 x - 5 \right)}} - \frac{49 \operatorname{atan}{\left(5 x \right)}}{\left(7 x - 5\right)^{2} \log{\left(7 x - 5 \right)}} - \frac{49 \operatorname{atan}{\left(5 x \right)}}{\left(7 x - 5\right)^{2} \log{\left(7 x - 5 \right)}^{2}}\right) \log{\left(7 x - 5 \right)}^{\operatorname{atan}{\left(5 x \right)}}$$
Tercera derivada
[src]
/ 3 2 \
atan(5*x) |/5*log(log(-5 + 7*x)) 7*atan(5*x) \ 250*log(log(-5 + 7*x)) /5*log(log(-5 + 7*x)) 7*atan(5*x) \ / 70 49*atan(5*x) 49*atan(5*x) 250*x*log(log(-5 + 7*x))\ 735 735 686*atan(5*x) 686*atan(5*x) 1029*atan(5*x) 25000*x *log(log(-5 + 7*x)) 5250*x |
log (-5 + 7*x)*||-------------------- + ------------------------| - ---------------------- - 3*|-------------------- + ------------------------|*|- ------------------------------------ + ------------------------- + -------------------------- + ------------------------| - ------------------------------------- - -------------------------------------- + ------------------------- + -------------------------- + -------------------------- + --------------------------- - -------------------------------------|
|| 2 (-5 + 7*x)*log(-5 + 7*x)| 2 | 2 (-5 + 7*x)*log(-5 + 7*x)| | / 2\ 2 2 2 2 | / 2\ 2 / 2\ 2 2 3 3 3 3 2 3 2 |
|\ 1 + 25*x / / 2\ \ 1 + 25*x / | \1 + 25*x /*(-5 + 7*x)*log(-5 + 7*x) (-5 + 7*x) *log(-5 + 7*x) (-5 + 7*x) *log (-5 + 7*x) / 2\ | \1 + 25*x /*(-5 + 7*x) *log(-5 + 7*x) \1 + 25*x /*(-5 + 7*x) *log (-5 + 7*x) (-5 + 7*x) *log(-5 + 7*x) (-5 + 7*x) *log (-5 + 7*x) (-5 + 7*x) *log (-5 + 7*x) / 2\ / 2\ |
\ \1 + 25*x / \ \1 + 25*x / / \1 + 25*x / \1 + 25*x / *(-5 + 7*x)*log(-5 + 7*x)/
$$\left(\frac{25000 x^{2} \log{\left(\log{\left(7 x - 5 \right)} \right)}}{\left(25 x^{2} + 1\right)^{3}} - \frac{5250 x}{\left(7 x - 5\right) \left(25 x^{2} + 1\right)^{2} \log{\left(7 x - 5 \right)}} + \left(\frac{5 \log{\left(\log{\left(7 x - 5 \right)} \right)}}{25 x^{2} + 1} + \frac{7 \operatorname{atan}{\left(5 x \right)}}{\left(7 x - 5\right) \log{\left(7 x - 5 \right)}}\right)^{3} - 3 \left(\frac{5 \log{\left(\log{\left(7 x - 5 \right)} \right)}}{25 x^{2} + 1} + \frac{7 \operatorname{atan}{\left(5 x \right)}}{\left(7 x - 5\right) \log{\left(7 x - 5 \right)}}\right) \left(\frac{250 x \log{\left(\log{\left(7 x - 5 \right)} \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{70}{\left(7 x - 5\right) \left(25 x^{2} + 1\right) \log{\left(7 x - 5 \right)}} + \frac{49 \operatorname{atan}{\left(5 x \right)}}{\left(7 x - 5\right)^{2} \log{\left(7 x - 5 \right)}} + \frac{49 \operatorname{atan}{\left(5 x \right)}}{\left(7 x - 5\right)^{2} \log{\left(7 x - 5 \right)}^{2}}\right) - \frac{250 \log{\left(\log{\left(7 x - 5 \right)} \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{735}{\left(7 x - 5\right)^{2} \left(25 x^{2} + 1\right) \log{\left(7 x - 5 \right)}} - \frac{735}{\left(7 x - 5\right)^{2} \left(25 x^{2} + 1\right) \log{\left(7 x - 5 \right)}^{2}} + \frac{686 \operatorname{atan}{\left(5 x \right)}}{\left(7 x - 5\right)^{3} \log{\left(7 x - 5 \right)}} + \frac{1029 \operatorname{atan}{\left(5 x \right)}}{\left(7 x - 5\right)^{3} \log{\left(7 x - 5 \right)}^{2}} + \frac{686 \operatorname{atan}{\left(5 x \right)}}{\left(7 x - 5\right)^{3} \log{\left(7 x - 5 \right)}^{3}}\right) \log{\left(7 x - 5 \right)}^{\operatorname{atan}{\left(5 x \right)}}$$
Gráfico