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 x*e^(1/x)
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Derivada de sin(2*x+3)
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Derivada de e^y
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Derivada de e^x-e^-x
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Expresiones idénticas
- (x^sqrt(x))^sin(x)
- (x en el grado raíz cuadrada de (x)) en el grado seno de (x)
- (x^√(x))^sin(x)
- (xsqrt(x))sin(x)
- xsqrtxsinx
- x^sqrtx^sinx
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Expresiones semejantes
- (x^sqrt(x))^sinx
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x)^3+1
- sqrt((1+x)/(1-x))
- sqrt(x-1)/(sqrt(x^2)-x-1)
- sqrt(x)*i^n*(sqrt(x)+sqrt(x+1))
- sqrt(x)/(x+2)
- Seno sin
- sin(2*x+3)
- sin^3x
- sin(8*x)
- sin(x)+(3*x)^6
- sin(v)
Derivada de (x^sqrt(x))^sin(x)
Solución
Ha introducido
[src]
sin(x) / ___\ | \/ x | \x /
$$\left(x^{\sqrt{x}}\right)^{\sin{\left(x \right)}}$$
(x^(sqrt(x)))^sin(x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
sin(x)
/ ___\ / / ___\\
| \/ x | |/ 1 log(x)\ | \/ x ||
\x / *||----- + -------|*sin(x) + cos(x)*log\x /|
|| ___ ___| |
\\\/ x 2*\/ x / /
$$\left(\left(\frac{\log{\left(x \right)}}{2 \sqrt{x}} + \frac{1}{\sqrt{x}}\right) \sin{\left(x \right)} + \log{\left(x^{\sqrt{x}} \right)} \cos{\left(x \right)}\right) \left(x^{\sqrt{x}}\right)^{\sin{\left(x \right)}}$$
Segunda derivada
[src]
/ 2 \
|/ / ___\ \ |
|| | \/ x | (2 + log(x))*sin(x)| |
sin(x) ||2*cos(x)*log\x / + -------------------| |
/ ___\ || ___ | / ___\ |
| \/ x | |\ \/ x / | \/ x | (2 + log(x))*cos(x) log(x)*sin(x)|
\x / *|--------------------------------------------- - log\x /*sin(x) + ------------------- - -------------|
| 4 ___ 3/2 |
\ \/ x 4*x /
$$\left(\frac{\left(2 \log{\left(x^{\sqrt{x}} \right)} \cos{\left(x \right)} + \frac{\left(\log{\left(x \right)} + 2\right) \sin{\left(x \right)}}{\sqrt{x}}\right)^{2}}{4} - \log{\left(x^{\sqrt{x}} \right)} \sin{\left(x \right)} + \frac{\left(\log{\left(x \right)} + 2\right) \cos{\left(x \right)}}{\sqrt{x}} - \frac{\log{\left(x \right)} \sin{\left(x \right)}}{4 x^{\frac{3}{2}}}\right) \left(x^{\sqrt{x}}\right)^{\sin{\left(x \right)}}$$
Tercera derivada
[src]
/ 3 \
|/ / ___\ \ / / ___\ \ / / ___\ \ |
|| | \/ x | (2 + log(x))*sin(x)| | | \/ x | (2 + log(x))*sin(x)| | | \/ x | log(x)*sin(x) 4*(2 + log(x))*cos(x)| |
sin(x) ||2*cos(x)*log\x / + -------------------| 3*|2*cos(x)*log\x / + -------------------|*|4*log\x /*sin(x) + ------------- - ---------------------| |
/ ___\ || ___ | / ___\ | ___ | | 3/2 ___ | |
| \/ x | |\ \/ x / | \/ x | \ \/ x / \ x \/ x / sin(x) 3*(2 + log(x))*sin(x) 3*cos(x)*log(x) 3*log(x)*sin(x)|
\x / *|--------------------------------------------- - cos(x)*log\x / - ------------------------------------------------------------------------------------------------------------- - ------ - --------------------- - --------------- + ---------------|
| 8 8 5/2 ___ 3/2 5/2 |
\ 4*x 2*\/ x 4*x 8*x /
$$\left(\frac{\left(2 \log{\left(x^{\sqrt{x}} \right)} \cos{\left(x \right)} + \frac{\left(\log{\left(x \right)} + 2\right) \sin{\left(x \right)}}{\sqrt{x}}\right)^{3}}{8} - \frac{3 \left(2 \log{\left(x^{\sqrt{x}} \right)} \cos{\left(x \right)} + \frac{\left(\log{\left(x \right)} + 2\right) \sin{\left(x \right)}}{\sqrt{x}}\right) \left(4 \log{\left(x^{\sqrt{x}} \right)} \sin{\left(x \right)} - \frac{4 \left(\log{\left(x \right)} + 2\right) \cos{\left(x \right)}}{\sqrt{x}} + \frac{\log{\left(x \right)} \sin{\left(x \right)}}{x^{\frac{3}{2}}}\right)}{8} - \log{\left(x^{\sqrt{x}} \right)} \cos{\left(x \right)} - \frac{3 \left(\log{\left(x \right)} + 2\right) \sin{\left(x \right)}}{2 \sqrt{x}} - \frac{3 \log{\left(x \right)} \cos{\left(x \right)}}{4 x^{\frac{3}{2}}} + \frac{3 \log{\left(x \right)} \sin{\left(x \right)}}{8 x^{\frac{5}{2}}} - \frac{\sin{\left(x \right)}}{4 x^{\frac{5}{2}}}\right) \left(x^{\sqrt{x}}\right)^{\sin{\left(x \right)}}$$
Gráfico