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 e^-1
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Derivada de (x^2)'
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Derivada de y
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Derivada de (x^5+1)
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Expresiones idénticas
- (x/sinx)^cosx
- (x dividir por seno de x) en el grado coseno de x
- (x/sinx)cosx
- x/sinxcosx
- x/sinx^cosx
- (x dividir por sinx)^cosx
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Expresiones con funciones
- sinx
- sinx+2cosx
- sinx*log5x
- sinx^sinx
- sinx/(2+cosx)
- sinx/(3-2cos(x))
- cosx
- cosx/lnx
Derivada de (x/sinx)^cosx
Solución
Ha introducido
[src]
cos(x) / x \ |------| \sin(x)/
$$\left(\frac{x}{\sin{\left(x \right)}}\right)^{\cos{\left(x \right)}}$$
(x/sin(x))^cos(x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ / 1 x*cos(x)\ \
| |------ - --------|*cos(x)*sin(x)|
cos(x) | |sin(x) 2 | |
/ x \ | / x \ \ sin (x) / |
|------| *|- log|------|*sin(x) + ---------------------------------|
\sin(x)/ \ \sin(x)/ x /
$$\left(\frac{x}{\sin{\left(x \right)}}\right)^{\cos{\left(x \right)}} \left(- \log{\left(\frac{x}{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\left(- \frac{x \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{1}{\sin{\left(x \right)}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{x}\right)$$
Segunda derivada
[src]
/ / 2 \ \
| 2 | 2*cos(x) 2*x*cos (x)| |
|/ / x*cos(x)\ \ |x - -------- + -----------|*cos(x) / x*cos(x)\ / x*cos(x)\ 2 / x*cos(x)\|
cos(x) || |-1 + --------|*cos(x)| | sin(x) 2 | |-1 + --------|*cos(x) 2*|-1 + --------|*sin(x) cos (x)*|-1 + --------||
/ x \ || / x \ \ sin(x) / | / x \ \ sin (x) / \ sin(x) / \ sin(x) / \ sin(x) /|
|------| *||log|------|*sin(x) + ----------------------| - cos(x)*log|------| + ----------------------------------- + ---------------------- + ------------------------ - -----------------------|
\sin(x)/ |\ \sin(x)/ x / \sin(x)/ x 2 x x*sin(x) |
\ x /
$$\left(\frac{x}{\sin{\left(x \right)}}\right)^{\cos{\left(x \right)}} \left(\left(\log{\left(\frac{x}{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x}\right)^{2} - \log{\left(\frac{x}{\sin{\left(x \right)}} \right)} \cos{\left(x \right)} + \frac{2 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \sin{\left(x \right)}}{x} - \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos^{2}{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{\left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \cos{\left(x \right)}}{x} + \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x^{2}}\right)$$
Tercera derivada
[src]
/ / / 2 \ \ / 2 3 \ / 2 \ / 2 \ / 2 \ \
| 3 | | 2*cos(x) 2*x*cos (x)| | | 6*cos (x) 5*x*cos(x) 6*x*cos (x)| | 2*cos(x) 2*x*cos (x)| | 2*cos(x) 2*x*cos (x)| 2 | 2*cos(x) 2*x*cos (x)| |
|/ / x*cos(x)\ \ / / x*cos(x)\ \ | |x - -------- + -----------|*cos(x) / x*cos(x)\ / x*cos(x)\ 2 / x*cos(x)\| |-3 - --------- + ---------- + -----------|*cos(x) / x*cos(x)\ / x*cos(x)\ 2*|x - -------- + -----------|*cos(x) 3*|x - -------- + -----------|*sin(x) / x*cos(x)\ 2*cos (x)*|x - -------- + -----------| 2 / x*cos(x)\|
cos(x) || |-1 + --------|*cos(x)| | |-1 + --------|*cos(x)| | | sin(x) 2 | |-1 + --------|*cos(x) 2*|-1 + --------|*sin(x) cos (x)*|-1 + --------|| | 2 sin(x) 3 | 7*|-1 + --------|*cos(x) 2*|-1 + --------|*cos(x) | sin(x) 2 | | sin(x) 2 | 3*|-1 + --------|*sin(x) | sin(x) 2 | 2*cos (x)*|-1 + --------||
/ x \ || / x \ \ sin(x) / | / x \ | / x \ \ sin(x) / | | / x \ \ sin (x) / \ sin(x) / \ sin(x) / \ sin(x) /| \ sin (x) sin (x) / \ sin(x) / \ sin(x) / \ sin (x) / \ sin (x) / \ sin(x) / \ sin (x) / \ sin(x) /|
-|------| *||log|------|*sin(x) + ----------------------| - log|------|*sin(x) + 3*|log|------|*sin(x) + ----------------------|*|- cos(x)*log|------| + ----------------------------------- + ---------------------- + ------------------------ - -----------------------| + -------------------------------------------------- - ------------------------ + ------------------------ + ------------------------------------- + ------------------------------------- + ------------------------ - -------------------------------------- - -------------------------|
\sin(x)/ |\ \sin(x)/ x / \sin(x)/ \ \sin(x)/ x / | \sin(x)/ x 2 x x*sin(x) | x x 3 2 x 2 x*sin(x) 2 |
\ \ x / x x x x *sin(x) /
$$- \left(\frac{x}{\sin{\left(x \right)}}\right)^{\cos{\left(x \right)}} \left(\left(\log{\left(\frac{x}{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x}\right)^{3} + 3 \left(\log{\left(\frac{x}{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x}\right) \left(- \log{\left(\frac{x}{\sin{\left(x \right)}} \right)} \cos{\left(x \right)} + \frac{2 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \sin{\left(x \right)}}{x} - \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos^{2}{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{\left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \cos{\left(x \right)}}{x} + \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x^{2}}\right) - \log{\left(\frac{x}{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} - \frac{7 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x} + \frac{3 \left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin{\left(x \right)}}{x} - \frac{2 \left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \cos^{2}{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{\left(\frac{5 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{6 x \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - 3 - \frac{6 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}{x} + \frac{3 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \sin{\left(x \right)}}{x^{2}} - \frac{2 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos^{2}{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2 \left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \cos{\left(x \right)}}{x^{2}} + \frac{2 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x^{3}}\right)$$
Gráfico