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
-
¿Cómo usar?
- Derivada de:
-
Derivada de x^-(4/5)
-
Derivada de x^-8
-
Derivada de x^2/lnx
-
Derivada de √x+2
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Expresiones idénticas
- x/((ln(ch(x)))^a)
- x dividir por ((ln(ch(x))) en el grado a)
- x/((ln(ch(x)))a)
- x/lnchxa
- x/lnchx^a
- x dividir por ((ln(ch(x)))^a)
-
Expresiones con funciones
- ln
- ln(x/5)
- ln(e^(2*x)+1)
- ln(x+sqrt(a^2+x^2))
- ln(x+8)
- ln(x+1)²
Derivada de x/((ln(ch(x)))^a)
Solución
Ha introducido
[src]
x ------------- a log (cosh(x))
$$\frac{x}{\log{\left(\cosh{\left(x \right)} \right)}^{a}}$$
x/log(cosh(x))^a
Primera derivada
[src]
-a
1 a*x*log (cosh(x))*sinh(x)
------------- - --------------------------
a cosh(x)*log(cosh(x))
log (cosh(x))
$$- \frac{a x \log{\left(\cosh{\left(x \right)} \right)}^{- a} \sinh{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)}} + \frac{1}{\log{\left(\cosh{\left(x \right)} \right)}^{a}}$$
Segunda derivada
[src]
/ / 2 2 2 \ \
-a | | sinh (x) sinh (x) a*sinh (x) | 2*sinh(x)|
a*log (cosh(x))*|x*|-1 + -------- + --------------------- + ---------------------| - ---------|
| | 2 2 2 | cosh(x) |
\ \ cosh (x) cosh (x)*log(cosh(x)) cosh (x)*log(cosh(x))/ /
------------------------------------------------------------------------------------------------
log(cosh(x))
$$\frac{a \left(x \left(\frac{a \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}} + \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} - 1 + \frac{\sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}}\right) - \frac{2 \sinh{\left(x \right)}}{\cosh{\left(x \right)}}\right) \log{\left(\cosh{\left(x \right)} \right)}^{- a}}{\log{\left(\cosh{\left(x \right)} \right)}}$$
Tercera derivada
[src]
/ / 2 2 2 2 2 2 2 \ \
| | 3 3*a 2*sinh (x) 2*sinh (x) 3*sinh (x) a *sinh (x) 3*a*sinh (x) 3*a*sinh (x) | |
| x*|-2 - ------------ - ------------ + ---------- + ---------------------- + --------------------- + ---------------------- + --------------------- + ----------------------|*sinh(x) |
| 2 2 | log(cosh(x)) log(cosh(x)) 2 2 2 2 2 2 2 2 2 | 2 |
-a | 3*sinh (x) 3*sinh (x) \ cosh (x) cosh (x)*log (cosh(x)) cosh (x)*log(cosh(x)) cosh (x)*log (cosh(x)) cosh (x)*log(cosh(x)) cosh (x)*log (cosh(x))/ 3*a*sinh (x) |
a*log (cosh(x))*|-3 + ---------- + --------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------|
| 2 2 cosh(x) 2 |
\ cosh (x) cosh (x)*log(cosh(x)) cosh (x)*log(cosh(x))/
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(cosh(x))
$$\frac{a \left(\frac{3 a \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}} - \frac{x \left(\frac{a^{2} \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)}^{2} \cosh^{2}{\left(x \right)}} + \frac{3 a \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}} - \frac{3 a}{\log{\left(\cosh{\left(x \right)} \right)}} + \frac{3 a \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)}^{2} \cosh^{2}{\left(x \right)}} + \frac{2 \sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} - 2 + \frac{3 \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}} - \frac{3}{\log{\left(\cosh{\left(x \right)} \right)}} + \frac{2 \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)}^{2} \cosh^{2}{\left(x \right)}}\right) \sinh{\left(x \right)}}{\cosh{\left(x \right)}} + \frac{3 \sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} - 3 + \frac{3 \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}}\right) \log{\left(\cosh{\left(x \right)} \right)}^{- a}}{\log{\left(\cosh{\left(x \right)} \right)}}$$