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 6/x
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Derivada de e^(x/2)
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Derivada de (x-1)/(x+1)
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Derivada de -3/x
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Expresiones idénticas
- y=(lnx)^ctg(siete ·x)
- y es igual a (lnx) en el grado ctg(7·x)
- y es igual a (lnx) en el grado ctg(siete ·x)
- y=(lnx)ctg(7·x)
- y=lnxctg7·x
- y=lnx^ctg7·x
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Expresiones con funciones
- lnx
- lnx-x
- lnx-x^3
- lnx^sinx
- lnx+sinx
- lnx/e^x^2
- ctg
- ctg(x/3)
- ctg4x
- ctg(1/x)
- ctg(2x+1)
- ctg(x^2)
Derivada de y=(lnx)^ctg(7·x)
Solución
Ha introducido
[src]
cot(7*x) log (x)
$$\log{\left(x \right)}^{\cot{\left(7 x \right)}}$$
log(x)^cot(7*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
cot(7*x) // 2 \ cot(7*x)\
log (x)*|\-7 - 7*cot (7*x)/*log(log(x)) + --------|
\ x*log(x)/
$$\left(\left(- 7 \cot^{2}{\left(7 x \right)} - 7\right) \log{\left(\log{\left(x \right)} \right)} + \frac{\cot{\left(7 x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\cot{\left(7 x \right)}}$$
Segunda derivada
[src]
/ 2 / 2 \ \
cot(7*x) |/ / 2 \ cot(7*x)\ cot(7*x) cot(7*x) 14*\1 + cot (7*x)/ / 2 \ |
log (x)*||7*\1 + cot (7*x)/*log(log(x)) - --------| - --------- - ---------- - ------------------ + 98*\1 + cot (7*x)/*cot(7*x)*log(log(x))|
|\ x*log(x)/ 2 2 2 x*log(x) |
\ x *log(x) x *log (x) /
$$\left(\left(7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} - \frac{\cot{\left(7 x \right)}}{x \log{\left(x \right)}}\right)^{2} + 98 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} \cot{\left(7 x \right)} - \frac{14 \left(\cot^{2}{\left(7 x \right)} + 1\right)}{x \log{\left(x \right)}} - \frac{\cot{\left(7 x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\cot{\left(7 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{\cot{\left(7 x \right)}}$$
Tercera derivada
[src]
/ 3 2 / / 2 \\ / 2 \ / 2 \ / 2 \ \
cot(7*x) | / / 2 \ cot(7*x)\ / 2 \ / / 2 \ cot(7*x)\ | cot(7*x) cot(7*x) / 2 \ 14*\1 + cot (7*x)/| 2 / 2 \ 2*cot(7*x) 2*cot(7*x) 3*cot(7*x) 21*\1 + cot (7*x)/ 21*\1 + cot (7*x)/ 294*\1 + cot (7*x)/*cot(7*x)|
log (x)*|- |7*\1 + cot (7*x)/*log(log(x)) - --------| - 686*\1 + cot (7*x)/ *log(log(x)) + 3*|7*\1 + cot (7*x)/*log(log(x)) - --------|*|--------- + ---------- - 98*\1 + cot (7*x)/*cot(7*x)*log(log(x)) + ------------------| - 1372*cot (7*x)*\1 + cot (7*x)/*log(log(x)) + ---------- + ---------- + ---------- + ------------------ + ------------------ + ----------------------------|
| \ x*log(x)/ \ x*log(x)/ | 2 2 2 x*log(x) | 3 3 3 3 2 2 2 2 x*log(x) |
\ \x *log(x) x *log (x) / x *log(x) x *log (x) x *log (x) x *log(x) x *log (x) /
$$\left(- \left(7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} - \frac{\cot{\left(7 x \right)}}{x \log{\left(x \right)}}\right)^{3} + 3 \left(7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} - \frac{\cot{\left(7 x \right)}}{x \log{\left(x \right)}}\right) \left(- 98 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} \cot{\left(7 x \right)} + \frac{14 \left(\cot^{2}{\left(7 x \right)} + 1\right)}{x \log{\left(x \right)}} + \frac{\cot{\left(7 x \right)}}{x^{2} \log{\left(x \right)}} + \frac{\cot{\left(7 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) - 686 \left(\cot^{2}{\left(7 x \right)} + 1\right)^{2} \log{\left(\log{\left(x \right)} \right)} - 1372 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} \cot^{2}{\left(7 x \right)} + \frac{294 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cot{\left(7 x \right)}}{x \log{\left(x \right)}} + \frac{21 \left(\cot^{2}{\left(7 x \right)} + 1\right)}{x^{2} \log{\left(x \right)}} + \frac{21 \left(\cot^{2}{\left(7 x \right)} + 1\right)}{x^{2} \log{\left(x \right)}^{2}} + \frac{2 \cot{\left(7 x \right)}}{x^{3} \log{\left(x \right)}} + \frac{3 \cot{\left(7 x \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{2 \cot{\left(7 x \right)}}{x^{3} \log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{\cot{\left(7 x \right)}}$$
Gráfico