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
-
¿Cómo usar?
- Derivada de:
-
Derivada de x^-8
-
Derivada de x^2/lnx
-
Derivada de √x+2
-
Derivada de (t^(2)+1)÷(t^(1÷2)-1)
- Ecuación diferencial:
- y'
-
Expresiones idénticas
- y'=(tgx)^(ln3x)
- y signo de prima para el primer (1) orden es igual a (tgx) en el grado (ln3x)
- y'=(tgx)(ln3x)
- y'=tgxln3x
- y'=tgx^ln3x
Derivada de y'=(tgx)^(ln3x)
Solución
Ha introducido
[src]
log(3*x) tan (x)
$$\tan^{\log{\left(3 x \right)}}{\left(x \right)}$$
tan(x)^log(3*x)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ / 2 \ \
log(3*x) |log(tan(x)) \1 + tan (x)/*log(3*x)|
tan (x)*|----------- + ----------------------|
\ x tan(x) /
$$\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x}\right) \tan^{\log{\left(3 x \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \|
log(3*x) ||log(tan(x)) \1 + tan (x)/*log(3*x)| log(tan(x)) / 2 \ \1 + tan (x)/ *log(3*x) 2*\1 + tan (x)/|
tan (x)*||----------- + ----------------------| - ----------- + 2*\1 + tan (x)/*log(3*x) - ----------------------- + ---------------|
|\ x tan(x) / 2 2 x*tan(x) |
\ x tan (x) /
$$\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x}\right)^{2} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(3 x \right)}}{\tan^{2}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x \tan{\left(x \right)}} - \frac{\log{\left(\tan{\left(x \right)} \right)}}{x^{2}}\right) \tan^{\log{\left(3 x \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 2 2 3 \
|/ / 2 \ \ / / 2 \ \ | / 2 \ / 2 \| / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ |
log(3*x) ||log(tan(x)) \1 + tan (x)/*log(3*x)| |log(tan(x)) \1 + tan (x)/*log(3*x)| |log(tan(x)) / 2 \ \1 + tan (x)/ *log(3*x) 2*\1 + tan (x)/| 2*log(tan(x)) 6*\1 + tan (x)/ 4*\1 + tan (x)/ *log(3*x) 3*\1 + tan (x)/ 3*\1 + tan (x)/ 2*\1 + tan (x)/ *log(3*x) / 2 \ |
tan (x)*||----------- + ----------------------| - 3*|----------- + ----------------------|*|----------- - 2*\1 + tan (x)/*log(3*x) + ----------------------- - ---------------| + ------------- + --------------- - ------------------------- - ---------------- - --------------- + ------------------------- + 4*\1 + tan (x)/*log(3*x)*tan(x)|
|\ x tan(x) / \ x tan(x) / | 2 2 x*tan(x) | 3 x tan(x) 2 2 3 |
\ \ x tan (x) / x x*tan (x) x *tan(x) tan (x) /
$$\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(3 x \right)}}{\tan^{2}{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x \tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x^{2}}\right) + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \log{\left(3 x \right)}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(3 x \right)}}{\tan{\left(x \right)}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 x \right)} \tan{\left(x \right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{x \tan^{2}{\left(x \right)}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} \tan{\left(x \right)}} + \frac{2 \log{\left(\tan{\left(x \right)} \right)}}{x^{3}}\right) \tan^{\log{\left(3 x \right)}}{\left(x \right)}$$
3-я производная
[src]
/ 3 / 2 \ 2 2 3 \
|/ / 2 \ \ / / 2 \ \ | / 2 \ / 2 \| / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ |
log(3*x) ||log(tan(x)) \1 + tan (x)/*log(3*x)| |log(tan(x)) \1 + tan (x)/*log(3*x)| |log(tan(x)) / 2 \ \1 + tan (x)/ *log(3*x) 2*\1 + tan (x)/| 2*log(tan(x)) 6*\1 + tan (x)/ 4*\1 + tan (x)/ *log(3*x) 3*\1 + tan (x)/ 3*\1 + tan (x)/ 2*\1 + tan (x)/ *log(3*x) / 2 \ |
tan (x)*||----------- + ----------------------| - 3*|----------- + ----------------------|*|----------- - 2*\1 + tan (x)/*log(3*x) + ----------------------- - ---------------| + ------------- + --------------- - ------------------------- - ---------------- - --------------- + ------------------------- + 4*\1 + tan (x)/*log(3*x)*tan(x)|
|\ x tan(x) / \ x tan(x) / | 2 2 x*tan(x) | 3 x tan(x) 2 2 3 |
\ \ x tan (x) / x x*tan (x) x *tan(x) tan (x) /
$$\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(3 x \right)}}{\tan^{2}{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x \tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x^{2}}\right) + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \log{\left(3 x \right)}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(3 x \right)}}{\tan{\left(x \right)}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 x \right)} \tan{\left(x \right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{x \tan^{2}{\left(x \right)}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} \tan{\left(x \right)}} + \frac{2 \log{\left(\tan{\left(x \right)} \right)}}{x^{3}}\right) \tan^{\log{\left(3 x \right)}}{\left(x \right)}$$
Gráfico