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:
- Derivada de e^((3*x)^2)
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Derivada de d/dx(x)
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Derivada de (cos(x))^x^2
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Derivada de (8*x-15)^5
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Expresiones idénticas
- y=(x^ dos -cos5x)^(3x^ dos -4x+ uno)
- y es igual a (x al cuadrado menos coseno de 5x) en el grado (3x al cuadrado menos 4x más 1)
- y es igual a (x en el grado dos menos coseno de 5x) en el grado (3x en el grado dos menos 4x más uno)
- y=(x2-cos5x)(3x2-4x+1)
- y=x2-cos5x3x2-4x+1
- y=(x²-cos5x)^(3x²-4x+1)
- y=(x en el grado 2-cos5x) en el grado (3x en el grado 2-4x+1)
- y=x^2-cos5x^3x^2-4x+1
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Expresiones semejantes
- y=(x^2-cos5x)^(3x^2+4x+1)
- y=(x^2-cos5x)^(3x^2-4x-1)
- y=(x^2+cos5x)^(3x^2-4x+1)
Derivada de y=(x^2-cos5x)^(3x^2-4x+1)
Solución
Ha introducido
[src]
2
3*x - 4*x + 1
/ 2 \
\x - cos(5*x)/
$$\left(x^{2} - \cos{\left(5 x \right)}\right)^{\left(3 x^{2} - 4 x\right) + 1}$$
(x^2 - cos(5*x))^(3*x^2 - 4*x + 1)
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]
2
3*x - 4*x + 1 / / 2 \\
/ 2 \ | / 2 \ (2*x + 5*sin(5*x))*\3*x - 4*x + 1/|
\x - cos(5*x)/ *|(-4 + 6*x)*log\x - cos(5*x)/ + -----------------------------------|
| 2 |
\ x - cos(5*x) /
$$\left(x^{2} - \cos{\left(5 x \right)}\right)^{\left(3 x^{2} - 4 x\right) + 1} \left(\frac{\left(2 x + 5 \sin{\left(5 x \right)}\right) \left(\left(3 x^{2} - 4 x\right) + 1\right)}{x^{2} - \cos{\left(5 x \right)}} + \left(6 x - 4\right) \log{\left(x^{2} - \cos{\left(5 x \right)} \right)}\right)$$
Segunda derivada
[src]
2 / 2 \
1 - 4*x + 3*x |/ / 2\\ / 2\ 2 / 2\ |
/ 2 \ || / 2 \ (2*x + 5*sin(5*x))*\1 - 4*x + 3*x /| / 2 \ (2 + 25*cos(5*x))*\1 - 4*x + 3*x / (2*x + 5*sin(5*x)) *\1 - 4*x + 3*x / 4*(-2 + 3*x)*(2*x + 5*sin(5*x))|
\x - cos(5*x)/ *||2*(-2 + 3*x)*log\x - cos(5*x)/ + -----------------------------------| + 6*log\x - cos(5*x)/ + ---------------------------------- - ------------------------------------ + -------------------------------|
|| 2 | 2 2 2 |
|\ x - cos(5*x) / x - cos(5*x) / 2 \ x - cos(5*x) |
\ \x - cos(5*x)/ /
$$\left(x^{2} - \cos{\left(5 x \right)}\right)^{3 x^{2} - 4 x + 1} \left(- \frac{\left(2 x + 5 \sin{\left(5 x \right)}\right)^{2} \left(3 x^{2} - 4 x + 1\right)}{\left(x^{2} - \cos{\left(5 x \right)}\right)^{2}} + \frac{4 \left(2 x + 5 \sin{\left(5 x \right)}\right) \left(3 x - 2\right)}{x^{2} - \cos{\left(5 x \right)}} + \left(\frac{\left(2 x + 5 \sin{\left(5 x \right)}\right) \left(3 x^{2} - 4 x + 1\right)}{x^{2} - \cos{\left(5 x \right)}} + 2 \left(3 x - 2\right) \log{\left(x^{2} - \cos{\left(5 x \right)} \right)}\right)^{2} + 6 \log{\left(x^{2} - \cos{\left(5 x \right)} \right)} + \frac{\left(25 \cos{\left(5 x \right)} + 2\right) \left(3 x^{2} - 4 x + 1\right)}{x^{2} - \cos{\left(5 x \right)}}\right)$$
Tercera derivada
[src]
/ 2 3 / 2\ / 2\ \
| / 2\ 6*(2*x + 5*sin(5*x)) *(-2 + 3*x) 2*(2*x + 5*sin(5*x)) *\1 - 4*x + 3*x / 3*(2 + 25*cos(5*x))*(2*x + 5*sin(5*x))*\1 - 4*x + 3*x / |
| 36*x + 90*sin(5*x) - 125*\1 - 4*x + 3*x /*sin(5*x) + 6*(-2 + 3*x)*(2 + 25*cos(5*x)) - -------------------------------- + -------------------------------------- - ------------------------------------------------------- |
2 | 3 2 2 2 |
1 - 4*x + 3*x |/ / 2\\ x - cos(5*x) / 2 \ x - cos(5*x) / / 2\\ / / 2\ 2 / 2\ \|
/ 2 \ || / 2 \ (2*x + 5*sin(5*x))*\1 - 4*x + 3*x /| \x - cos(5*x)/ | / 2 \ (2*x + 5*sin(5*x))*\1 - 4*x + 3*x /| | / 2 \ (2 + 25*cos(5*x))*\1 - 4*x + 3*x / (2*x + 5*sin(5*x)) *\1 - 4*x + 3*x / 4*(-2 + 3*x)*(2*x + 5*sin(5*x))||
\x - cos(5*x)/ *||2*(-2 + 3*x)*log\x - cos(5*x)/ + -----------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 3*|2*(-2 + 3*x)*log\x - cos(5*x)/ + -----------------------------------|*|6*log\x - cos(5*x)/ + ---------------------------------- - ------------------------------------ + -------------------------------||
|| 2 | 2 | 2 | | 2 2 2 ||
|\ x - cos(5*x) / x - cos(5*x) \ x - cos(5*x) / | x - cos(5*x) / 2 \ x - cos(5*x) ||
\ \ \x - cos(5*x)/ //
$$\left(x^{2} - \cos{\left(5 x \right)}\right)^{3 x^{2} - 4 x + 1} \left(\left(\frac{\left(2 x + 5 \sin{\left(5 x \right)}\right) \left(3 x^{2} - 4 x + 1\right)}{x^{2} - \cos{\left(5 x \right)}} + 2 \left(3 x - 2\right) \log{\left(x^{2} - \cos{\left(5 x \right)} \right)}\right)^{3} + 3 \left(\frac{\left(2 x + 5 \sin{\left(5 x \right)}\right) \left(3 x^{2} - 4 x + 1\right)}{x^{2} - \cos{\left(5 x \right)}} + 2 \left(3 x - 2\right) \log{\left(x^{2} - \cos{\left(5 x \right)} \right)}\right) \left(- \frac{\left(2 x + 5 \sin{\left(5 x \right)}\right)^{2} \left(3 x^{2} - 4 x + 1\right)}{\left(x^{2} - \cos{\left(5 x \right)}\right)^{2}} + \frac{4 \left(2 x + 5 \sin{\left(5 x \right)}\right) \left(3 x - 2\right)}{x^{2} - \cos{\left(5 x \right)}} + 6 \log{\left(x^{2} - \cos{\left(5 x \right)} \right)} + \frac{\left(25 \cos{\left(5 x \right)} + 2\right) \left(3 x^{2} - 4 x + 1\right)}{x^{2} - \cos{\left(5 x \right)}}\right) + \frac{36 x + \frac{2 \left(2 x + 5 \sin{\left(5 x \right)}\right)^{3} \left(3 x^{2} - 4 x + 1\right)}{\left(x^{2} - \cos{\left(5 x \right)}\right)^{2}} - \frac{6 \left(2 x + 5 \sin{\left(5 x \right)}\right)^{2} \left(3 x - 2\right)}{x^{2} - \cos{\left(5 x \right)}} - \frac{3 \left(2 x + 5 \sin{\left(5 x \right)}\right) \left(25 \cos{\left(5 x \right)} + 2\right) \left(3 x^{2} - 4 x + 1\right)}{x^{2} - \cos{\left(5 x \right)}} + 6 \left(3 x - 2\right) \left(25 \cos{\left(5 x \right)} + 2\right) - 125 \left(3 x^{2} - 4 x + 1\right) \sin{\left(5 x \right)} + 90 \sin{\left(5 x \right)}}{x^{2} - \cos{\left(5 x \right)}}\right)$$