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 (-4)/x^2
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Derivada de 2/x²
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Derivada de -2*y
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Derivada de (3+2x)/(x-5)
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Expresiones idénticas
- x*exp(-x)(ctg(3x))^tg(x)
- x multiplicar por exponente de ( menos x)(ctg(3x)) en el grado tg(x)
- x*exp(-x)(ctg(3x))tg(x)
- x*exp-xctg3xtgx
- xexp(-x)(ctg(3x))^tg(x)
- xexp(-x)(ctg(3x))tg(x)
- xexp-xctg3xtgx
- xexp-xctg3x^tgx
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Expresiones semejantes
- x*exp(x)(ctg(3x))^tg(x)
Derivada de x*exp(-x)(ctg(3x))^tg(x)
Solución
Ha introducido
[src]
-x tan(x) x*e *cot (3*x)
$$x e^{- x} \cot^{\tan{\left(x \right)}}{\left(3 x \right)}$$
(x*exp(-x))*cot(3*x)^tan(x)
Solución detallada
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Se aplica la regla de la derivada parcial:
y .
Para calcular :
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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Según el principio, aplicamos: tenemos
; calculamos :
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de:
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Para calcular :
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Derivado es.
Ahora aplicamos la regla de la derivada de una divesión:
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Simplificamos:
Respuesta:
Primera derivada
[src]
/ / 2 \ \
tan(x) / -x -x\ tan(x) |/ 2 \ \-3 - 3*cot (3*x)/*tan(x)| -x
cot (3*x)*\- x*e + e / + x*cot (3*x)*|\1 + tan (x)/*log(cot(3*x)) + -------------------------|*e
\ cot(3*x) /
$$x \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(3 x \right)} \right)} + \frac{\left(- 3 \cot^{2}{\left(3 x \right)} - 3\right) \tan{\left(x \right)}}{\cot{\left(3 x \right)}}\right) e^{- x} \cot^{\tan{\left(x \right)}}{\left(3 x \right)} + \left(- x e^{- x} + e^{- x}\right) \cot^{\tan{\left(x \right)}}{\left(3 x \right)}$$
Segunda derivada
[src]
/ / 2 2 \ \
| |/ / 2 \ \ / 2 \ / 2 \ / 2 \ | / / 2 \ \|
tan(x) | ||/ 2 \ 3*\1 + cot (3*x)/*tan(x)| / 2 \ 9*\1 + cot (3*x)/ *tan(x) 6*\1 + cot (3*x)/*\1 + tan (x)/ / 2 \ | |/ 2 \ 3*\1 + cot (3*x)/*tan(x)|| -x
cot (3*x)*|-2 + x + x*||\1 + tan (x)/*log(cot(3*x)) - ------------------------| + 18*\1 + cot (3*x)/*tan(x) - ------------------------- - ------------------------------- + 2*\1 + tan (x)/*log(cot(3*x))*tan(x)| - 2*(-1 + x)*|\1 + tan (x)/*log(cot(3*x)) - ------------------------||*e
| |\ cot(3*x) / 2 cot(3*x) | \ cot(3*x) /|
\ \ cot (3*x) / /
$$\left(x \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(3 x \right)} \right)} - \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \tan{\left(x \right)}}{\cot{\left(3 x \right)}}\right)^{2} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(3 x \right)} \right)} \tan{\left(x \right)} - \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\cot^{2}{\left(3 x \right)}} + 18 \left(\cot^{2}{\left(3 x \right)} + 1\right) \tan{\left(x \right)}\right) + x - 2 \left(x - 1\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(3 x \right)} \right)} - \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \tan{\left(x \right)}}{\cot{\left(3 x \right)}}\right) - 2\right) e^{- x} \cot^{\tan{\left(x \right)}}{\left(3 x \right)}$$
Tercera derivada
[src]
/ / 3 / 2 \ 3 2 2 \ / 2 2 \ \
| |/ / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ / 2 \ | 2 / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ | |/ / 2 \ \ / 2 \ / 2 \ / 2 \ | / / 2 \ \|
tan(x) | ||/ 2 \ 3*\1 + cot (3*x)/*tan(x)| |/ 2 \ 3*\1 + cot (3*x)/*tan(x)| | / 2 \ / 2 \ 6*\1 + cot (3*x)/*\1 + tan (x)/ 9*\1 + cot (3*x)/ *tan(x)| / 2 \ / 2 \ / 2 \ / 2 \ 54*\1 + cot (3*x)/ *tan(x) 27*\1 + cot (3*x)/ *\1 + tan (x)/ 2 / 2 \ 108*\1 + cot (3*x)/ *tan(x) 18*\1 + cot (3*x)/*\1 + tan (x)/*tan(x)| ||/ 2 \ 3*\1 + cot (3*x)/*tan(x)| / 2 \ 9*\1 + cot (3*x)/ *tan(x) 6*\1 + cot (3*x)/*\1 + tan (x)/ / 2 \ | |/ 2 \ 3*\1 + cot (3*x)/*tan(x)|| -x
cot (3*x)*|3 - x + x*||\1 + tan (x)/*log(cot(3*x)) - ------------------------| - 3*|\1 + tan (x)/*log(cot(3*x)) - ------------------------|*|- 18*\1 + cot (3*x)/*tan(x) - 2*\1 + tan (x)/*log(cot(3*x))*tan(x) + ------------------------------- + -------------------------| + 2*\1 + tan (x)/ *log(cot(3*x)) + 54*\1 + cot (3*x)/*\1 + tan (x)/ - 108*\1 + cot (3*x)/*cot(3*x)*tan(x) - -------------------------- - --------------------------------- + 4*tan (x)*\1 + tan (x)/*log(cot(3*x)) + --------------------------- - ---------------------------------------| - 3*(-1 + x)*||\1 + tan (x)/*log(cot(3*x)) - ------------------------| + 18*\1 + cot (3*x)/*tan(x) - ------------------------- - ------------------------------- + 2*\1 + tan (x)/*log(cot(3*x))*tan(x)| + 3*(-2 + x)*|\1 + tan (x)/*log(cot(3*x)) - ------------------------||*e
| |\ cot(3*x) / \ cot(3*x) / | cot(3*x) 2 | 3 2 cot(3*x) cot(3*x) | |\ cot(3*x) / 2 cot(3*x) | \ cot(3*x) /|
\ \ \ cot (3*x) / cot (3*x) cot (3*x) / \ cot (3*x) / /
$$\left(x \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(3 x \right)} \right)} - \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \tan{\left(x \right)}}{\cot{\left(3 x \right)}}\right)^{3} - 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(3 x \right)} \right)} - \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \tan{\left(x \right)}}{\cot{\left(3 x \right)}}\right) \left(\frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(3 x \right)} \right)} \tan{\left(x \right)} + \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\cot^{2}{\left(3 x \right)}} - 18 \left(\cot^{2}{\left(3 x \right)} + 1\right) \tan{\left(x \right)}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\cot{\left(3 x \right)} \right)} - \frac{27 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} - \frac{18 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right) \tan{\left(x \right)}}{\cot{\left(3 x \right)}} + 54 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right) + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(3 x \right)} \right)} \tan^{2}{\left(x \right)} - \frac{54 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{3} \tan{\left(x \right)}}{\cot^{3}{\left(3 x \right)}} + \frac{108 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\cot{\left(3 x \right)}} - 108 \left(\cot^{2}{\left(3 x \right)} + 1\right) \tan{\left(x \right)} \cot{\left(3 x \right)}\right) - x + 3 \left(x - 2\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(3 x \right)} \right)} - \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \tan{\left(x \right)}}{\cot{\left(3 x \right)}}\right) - 3 \left(x - 1\right) \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(3 x \right)} \right)} - \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \tan{\left(x \right)}}{\cot{\left(3 x \right)}}\right)^{2} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(3 x \right)} \right)} \tan{\left(x \right)} - \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\cot^{2}{\left(3 x \right)}} + 18 \left(\cot^{2}{\left(3 x \right)} + 1\right) \tan{\left(x \right)}\right) + 3\right) e^{- x} \cot^{\tan{\left(x \right)}}{\left(3 x \right)}$$
Gráfico