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 (π-2x)³
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Derivada de y=e×
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Derivada de y*log(5*y-1)
- Derivada de y=ln((sqrt(x))+(sqrt(x+a)))
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Expresiones idénticas
- x^sqrt(sin3x)
- x en el grado raíz cuadrada de ( seno de 3x)
- x^√(sin3x)
- xsqrt(sin3x)
- xsqrtsin3x
- x^sqrtsin3x
Derivada de x^sqrt(sin3x)
Solución
Ha introducido
[src]
__________ \/ sin(3*x) x
$$x^{\sqrt{\sin{\left(3 x \right)}}}$$
x^(sqrt(sin(3*x)))
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
Primera derivada
[src]
__________ / __________ \
\/ sin(3*x) |\/ sin(3*x) 3*cos(3*x)*log(x)|
x *|------------ + -----------------|
| x __________ |
\ 2*\/ sin(3*x) /
$$x^{\sqrt{\sin{\left(3 x \right)}}} \left(\frac{3 \log{\left(x \right)} \cos{\left(3 x \right)}}{2 \sqrt{\sin{\left(3 x \right)}}} + \frac{\sqrt{\sin{\left(3 x \right)}}}{x}\right)$$
Segunda derivada
[src]
/ 2 \
|/ __________ \ |
||2*\/ sin(3*x) 3*cos(3*x)*log(x)| |
||-------------- + -----------------| |
__________ || x __________ | __________ __________ 2 |
\/ sin(3*x) |\ \/ sin(3*x) / \/ sin(3*x) 9*\/ sin(3*x) *log(x) 3*cos(3*x) 9*cos (3*x)*log(x)|
x *|------------------------------------- - ------------ - --------------------- + -------------- - ------------------|
| 4 2 2 __________ 3/2 |
\ x x*\/ sin(3*x) 4*sin (3*x) /
$$x^{\sqrt{\sin{\left(3 x \right)}}} \left(\frac{\left(\frac{3 \log{\left(x \right)} \cos{\left(3 x \right)}}{\sqrt{\sin{\left(3 x \right)}}} + \frac{2 \sqrt{\sin{\left(3 x \right)}}}{x}\right)^{2}}{4} - \frac{9 \log{\left(x \right)} \sqrt{\sin{\left(3 x \right)}}}{2} - \frac{9 \log{\left(x \right)} \cos^{2}{\left(3 x \right)}}{4 \sin^{\frac{3}{2}}{\left(3 x \right)}} + \frac{3 \cos{\left(3 x \right)}}{x \sqrt{\sin{\left(3 x \right)}}} - \frac{\sqrt{\sin{\left(3 x \right)}}}{x^{2}}\right)$$
Tercera derivada
[src]
/ 3 \
|/ __________ \ / __________ \ / __________ 2 \ |
||2*\/ sin(3*x) 3*cos(3*x)*log(x)| |2*\/ sin(3*x) 3*cos(3*x)*log(x)| |4*\/ sin(3*x) __________ 12*cos(3*x) 9*cos (3*x)*log(x)| |
||-------------- + -----------------| 3*|-------------- + -----------------|*|-------------- + 18*\/ sin(3*x) *log(x) - -------------- + ------------------| |
__________ || x __________ | __________ __________ | x __________ | | 2 __________ 3/2 | 2 3 |
\/ sin(3*x) |\ \/ sin(3*x) / 2*\/ sin(3*x) 27*\/ sin(3*x) \ \/ sin(3*x) / \ x x*\/ sin(3*x) sin (3*x) / 27*cos (3*x) 9*cos(3*x) 27*cos(3*x)*log(x) 81*cos (3*x)*log(x)|
x *|------------------------------------- + -------------- - --------------- - ---------------------------------------------------------------------------------------------------------------------- - --------------- - ----------------- + ------------------ + -------------------|
| 8 3 2*x 8 3/2 2 __________ __________ 5/2 |
\ x 4*x*sin (3*x) 2*x *\/ sin(3*x) 4*\/ sin(3*x) 8*sin (3*x) /
$$x^{\sqrt{\sin{\left(3 x \right)}}} \left(\frac{\left(\frac{3 \log{\left(x \right)} \cos{\left(3 x \right)}}{\sqrt{\sin{\left(3 x \right)}}} + \frac{2 \sqrt{\sin{\left(3 x \right)}}}{x}\right)^{3}}{8} - \frac{3 \left(\frac{3 \log{\left(x \right)} \cos{\left(3 x \right)}}{\sqrt{\sin{\left(3 x \right)}}} + \frac{2 \sqrt{\sin{\left(3 x \right)}}}{x}\right) \left(18 \log{\left(x \right)} \sqrt{\sin{\left(3 x \right)}} + \frac{9 \log{\left(x \right)} \cos^{2}{\left(3 x \right)}}{\sin^{\frac{3}{2}}{\left(3 x \right)}} - \frac{12 \cos{\left(3 x \right)}}{x \sqrt{\sin{\left(3 x \right)}}} + \frac{4 \sqrt{\sin{\left(3 x \right)}}}{x^{2}}\right)}{8} + \frac{27 \log{\left(x \right)} \cos{\left(3 x \right)}}{4 \sqrt{\sin{\left(3 x \right)}}} + \frac{81 \log{\left(x \right)} \cos^{3}{\left(3 x \right)}}{8 \sin^{\frac{5}{2}}{\left(3 x \right)}} - \frac{27 \sqrt{\sin{\left(3 x \right)}}}{2 x} - \frac{27 \cos^{2}{\left(3 x \right)}}{4 x \sin^{\frac{3}{2}}{\left(3 x \right)}} - \frac{9 \cos{\left(3 x \right)}}{2 x^{2} \sqrt{\sin{\left(3 x \right)}}} + \frac{2 \sqrt{\sin{\left(3 x \right)}}}{x^{3}}\right)$$
Gráfico