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 (3x^4-x)^7
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Derivada de (3x+6)^2
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Derivada de (1+cos(x))/(1-cos(x))
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Derivada de (2*x-9)/(x-5)
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Expresiones idénticas
- y=x^(dos ·x+sin(tres ·x))^(uno / dos)
- y es igual a x en el grado (2·x más seno de (3·x)) en el grado (1 dividir por 2)
- y es igual a x en el grado (dos ·x más seno de (tres ·x)) en el grado (uno dividir por dos)
- y=x(2·x+sin(3·x))(1/2)
- y=x2·x+sin3·x1/2
- y=x^2·x+sin3·x^1/2
- y=x^(2·x+sin(3·x))^(1 dividir por 2)
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Expresiones semejantes
- y=x^(2·x-sin(3·x))^(1/2)
Derivada de y=x^(2·x+sin(3·x))^(1/2)
Solución
Ha introducido
[src]
________________ \/ 2*x + sin(3*x) x
$$x^{\sqrt{2 x + \sin{\left(3 x \right)}}}$$
x^(sqrt(2*x + 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]
/ / 3*cos(3*x)\ \
________________ | ________________ |1 + ----------|*log(x)|
\/ 2*x + sin(3*x) |\/ 2*x + sin(3*x) \ 2 / |
x *|------------------ + -----------------------|
| x ________________ |
\ \/ 2*x + sin(3*x) /
$$x^{\sqrt{2 x + \sin{\left(3 x \right)}}} \left(\frac{\left(\frac{3 \cos{\left(3 x \right)}}{2} + 1\right) \log{\left(x \right)}}{\sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{\sqrt{2 x + \sin{\left(3 x \right)}}}{x}\right)$$
Segunda derivada
[src]
/ 2 \
|/ ________________ \ |
||2*\/ 2*x + sin(3*x) (2 + 3*cos(3*x))*log(x)| |
||-------------------- + -----------------------| |
________________ || x ________________ | ________________ 2 |
\/ 2*x + sin(3*x) |\ \/ 2*x + sin(3*x) / \/ 2*x + sin(3*x) 2 + 3*cos(3*x) 9*log(x)*sin(3*x) (2 + 3*cos(3*x)) *log(x)|
x *|------------------------------------------------- - ------------------ + -------------------- - -------------------- - ------------------------|
| 4 2 ________________ ________________ 3/2 |
\ x x*\/ 2*x + sin(3*x) 2*\/ 2*x + sin(3*x) 4*(2*x + sin(3*x)) /
$$x^{\sqrt{2 x + \sin{\left(3 x \right)}}} \left(\frac{\left(\frac{\left(3 \cos{\left(3 x \right)} + 2\right) \log{\left(x \right)}}{\sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{2 \sqrt{2 x + \sin{\left(3 x \right)}}}{x}\right)^{2}}{4} - \frac{9 \log{\left(x \right)} \sin{\left(3 x \right)}}{2 \sqrt{2 x + \sin{\left(3 x \right)}}} - \frac{\left(3 \cos{\left(3 x \right)} + 2\right)^{2} \log{\left(x \right)}}{4 \left(2 x + \sin{\left(3 x \right)}\right)^{\frac{3}{2}}} + \frac{3 \cos{\left(3 x \right)} + 2}{x \sqrt{2 x + \sin{\left(3 x \right)}}} - \frac{\sqrt{2 x + \sin{\left(3 x \right)}}}{x^{2}}\right)$$
Tercera derivada
[src]
/ 3 \
|/ ________________ \ / ________________ \ / ________________ 2 \ |
||2*\/ 2*x + sin(3*x) (2 + 3*cos(3*x))*log(x)| |2*\/ 2*x + sin(3*x) (2 + 3*cos(3*x))*log(x)| |4*\/ 2*x + sin(3*x) (2 + 3*cos(3*x)) *log(x) 4*(2 + 3*cos(3*x)) 18*log(x)*sin(3*x)| |
||-------------------- + -----------------------| 3*|-------------------- + -----------------------|*|-------------------- + ------------------------ - -------------------- + ------------------| |
________________ || x ________________ | ________________ | x ________________ | | 2 3/2 ________________ ________________| 2 3 |
\/ 2*x + sin(3*x) |\ \/ 2*x + sin(3*x) / 2*\/ 2*x + sin(3*x) \ \/ 2*x + sin(3*x) / \ x (2*x + sin(3*x)) x*\/ 2*x + sin(3*x) \/ 2*x + sin(3*x) / 27*sin(3*x) 27*cos(3*x)*log(x) 3*(2 + 3*cos(3*x)) 3*(2 + 3*cos(3*x)) 3*(2 + 3*cos(3*x)) *log(x) 27*(2 + 3*cos(3*x))*log(x)*sin(3*x)|
x *|------------------------------------------------- + -------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------ - ---------------------- - -------------------- - ----------------------- - ----------------------- + -------------------------- + -----------------------------------|
| 8 3 8 ________________ ________________ 2 ________________ 3/2 5/2 3/2 |
\ x 2*x*\/ 2*x + sin(3*x) 2*\/ 2*x + sin(3*x) 2*x *\/ 2*x + sin(3*x) 4*x*(2*x + sin(3*x)) 8*(2*x + sin(3*x)) 4*(2*x + sin(3*x)) /
$$x^{\sqrt{2 x + \sin{\left(3 x \right)}}} \left(\frac{\left(\frac{\left(3 \cos{\left(3 x \right)} + 2\right) \log{\left(x \right)}}{\sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{2 \sqrt{2 x + \sin{\left(3 x \right)}}}{x}\right)^{3}}{8} - \frac{3 \left(\frac{\left(3 \cos{\left(3 x \right)} + 2\right) \log{\left(x \right)}}{\sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{2 \sqrt{2 x + \sin{\left(3 x \right)}}}{x}\right) \left(\frac{18 \log{\left(x \right)} \sin{\left(3 x \right)}}{\sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{\left(3 \cos{\left(3 x \right)} + 2\right)^{2} \log{\left(x \right)}}{\left(2 x + \sin{\left(3 x \right)}\right)^{\frac{3}{2}}} - \frac{4 \left(3 \cos{\left(3 x \right)} + 2\right)}{x \sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{4 \sqrt{2 x + \sin{\left(3 x \right)}}}{x^{2}}\right)}{8} - \frac{27 \log{\left(x \right)} \cos{\left(3 x \right)}}{2 \sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{27 \left(3 \cos{\left(3 x \right)} + 2\right) \log{\left(x \right)} \sin{\left(3 x \right)}}{4 \left(2 x + \sin{\left(3 x \right)}\right)^{\frac{3}{2}}} + \frac{3 \left(3 \cos{\left(3 x \right)} + 2\right)^{3} \log{\left(x \right)}}{8 \left(2 x + \sin{\left(3 x \right)}\right)^{\frac{5}{2}}} - \frac{27 \sin{\left(3 x \right)}}{2 x \sqrt{2 x + \sin{\left(3 x \right)}}} - \frac{3 \left(3 \cos{\left(3 x \right)} + 2\right)^{2}}{4 x \left(2 x + \sin{\left(3 x \right)}\right)^{\frac{3}{2}}} - \frac{3 \left(3 \cos{\left(3 x \right)} + 2\right)}{2 x^{2} \sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{2 \sqrt{2 x + \sin{\left(3 x \right)}}}{x^{3}}\right)$$
Gráfico