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^-0,2
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Derivada de e-x
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Derivada de e^e
- Derivada de e^((3*x)^2)
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Expresiones idénticas
- y=x^(tg^ dos)x
- y es igual a x en el grado (tg al cuadrado )x
- y es igual a x en el grado (tg en el grado dos)x
- y=x(tg2)x
- y=xtg2x
- y=x^(tg²)x
- y=x en el grado (tg en el grado 2)x
- y=x^tg^2x
Derivada de y=x^(tg^2)x
Solución
Solución detallada
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
; calculamos :
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Según el principio, aplicamos: tenemos
Como resultado de:
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Respuesta:
Primera derivada
[src]
2 2 / 2 \
tan (x) tan (x) |tan (x) / 2 \ |
x + x*x *|------- + \2 + 2*tan (x)/*log(x)*tan(x)|
\ x /
$$x x^{\tan^{2}{\left(x \right)}} \left(\left(2 \tan^{2}{\left(x \right)} + 2\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{\tan^{2}{\left(x \right)}}{x}\right) + x^{\tan^{2}{\left(x \right)}}$$
Segunda derivada
[src]
2 / / 2 2 2 / 2 \ \ \
tan (x) | |/tan(x) / 2 \ \ 2 tan (x) / 2 \ 4*\1 + tan (x)/*tan(x) 2 / 2 \ | /tan(x) / 2 \ \ |
x *|x*||------ + 2*\1 + tan (x)/*log(x)| *tan (x) - ------- + 2*\1 + tan (x)/ *log(x) + ---------------------- + 4*tan (x)*\1 + tan (x)/*log(x)| + 2*|------ + 2*\1 + tan (x)/*log(x)|*tan(x)|
| |\ x / 2 x | \ x / |
\ \ x / /
$$x^{\tan^{2}{\left(x \right)}} \left(x \left(\left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} \tan^{2}{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{\tan^{2}{\left(x \right)}}{x^{2}}\right) + 2 \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \tan{\left(x \right)}\right)$$
Tercera derivada
[src]
/ / 2 \ \
2 | | 3 2 / 2 \ / 2 \ / 2 2 / 2 \ \ 2 / 2 \ 2 | 2 2 2 / 2 \ |
tan (x) | |/tan(x) / 2 \ \ 3 2*tan (x) 6*\1 + tan (x)/ 6*\1 + tan (x)/*tan(x) /tan(x) / 2 \ \ | tan (x) / 2 \ 4*\1 + tan (x)/*tan(x) 2 / 2 \ | 3 / 2 \ 12*tan (x)*\1 + tan (x)/ / 2 \ | 3*tan (x) /tan(x) / 2 \ \ 2 / 2 \ 12*\1 + tan (x)/*tan(x) 2 / 2 \ |
x *|x*||------ + 2*\1 + tan (x)/*log(x)| *tan (x) + --------- + ---------------- - ---------------------- + 3*|------ + 2*\1 + tan (x)/*log(x)|*|- ------- + 2*\1 + tan (x)/ *log(x) + ---------------------- + 4*tan (x)*\1 + tan (x)/*log(x)|*tan(x) + 8*tan (x)*\1 + tan (x)/*log(x) + ------------------------ + 16*\1 + tan (x)/ *log(x)*tan(x)| - --------- + 3*|------ + 2*\1 + tan (x)/*log(x)| *tan (x) + 6*\1 + tan (x)/ *log(x) + ----------------------- + 12*tan (x)*\1 + tan (x)/*log(x)|
| |\ x / 3 x 2 \ x / | 2 x | x | 2 \ x / x |
\ \ x x \ x / / x /
$$x^{\tan^{2}{\left(x \right)}} \left(x \left(\left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} \tan^{3}{\left(x \right)} + 3 \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{\tan^{2}{\left(x \right)}}{x^{2}}\right) \tan{\left(x \right)} + 16 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} \tan{\left(x \right)} + 8 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{3}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{x} + \frac{12 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{x} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{2}} + \frac{2 \tan^{2}{\left(x \right)}}{x^{3}}\right) + 3 \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} \tan^{2}{\left(x \right)} + 6 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 12 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{12 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{3 \tan^{2}{\left(x \right)}}{x^{2}}\right)$$