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:
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Derivada de 6/x
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Derivada de e^(x/2)
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Derivada de (x-1)/(x+1)
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Derivada de -3/x
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Expresiones idénticas
- (xtgx+lncosx)*tg(xtgx+lncosx)+lncos(xtgx+lncosx)
- (xtgx más ln coseno de x) multiplicar por tg(xtgx más ln coseno de x) más ln coseno de (xtgx más ln coseno de x)
- (xtgx+lncosx)tg(xtgx+lncosx)+lncos(xtgx+lncosx)
- xtgx+lncosxtgxtgx+lncosx+lncosxtgx+lncosx
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Expresiones semejantes
- (xtgx+lncosx)*tg(xtgx-lncosx)+lncos(xtgx+lncosx)
- (xtgx+lncosx)*tg(xtgx+lncosx)+lncos(xtgx-lncosx)
- (xtgx+lncosx)*tg(xtgx+lncosx)-lncos(xtgx+lncosx)
- (xtgx+lncosx)tg(xtgx+lncosx)+lncos(xtgx+lncosx)
- (xtgx-lncosx)*tg(xtgx+lncosx)+lncos(xtgx+lncosx)
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Expresiones con funciones
- xtgx
- xtgx/4
- xtgx+ctgx
- xtgx+4
- xtgx-2^x
- xtgx+ln(cosx)
- tg
- tg^3(x)
- tgx+sinx
- tg(x^3)
- tg5x^1/5
- tgx/(sinx-cosx)
- xtgx
- xtgx/4
- xtgx+ctgx
- xtgx+4
- xtgx-2^x
- xtgx+ln(cosx)
- xtgx
- xtgx/4
- xtgx+ctgx
- xtgx+4
- xtgx-2^x
- xtgx+ln(cosx)
Derivada de (xtgx+lncosx)*tg(xtgx+lncosx)+lncos(xtgx+lncosx)
Solución
Ha introducido
[src]
(x*tan(x) + log(cos(x)))*tan(x*tan(x) + log(cos(x))) + log(cos(x*tan(x) + log(cos(x))))
$$\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)}\right) \tan{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + \log{\left(\cos{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} \right)}$$
(x*tan(x) + log(cos(x)))*tan(x*tan(x) + log(cos(x))) + log(cos(x*tan(x) + log(cos(x))))
Primera derivada
[src]
/ / 2 \ sin(x) \
|x*\1 + tan (x)/ - ------ + tan(x)|*sin(x*tan(x) + log(cos(x)))
/ / 2 \ sin(x) \ / 2 \ / / 2 \ sin(x) \ \ cos(x) /
|x*\1 + tan (x)/ - ------ + tan(x)|*tan(x*tan(x) + log(cos(x))) + \1 + tan (x*tan(x) + log(cos(x)))/*(x*tan(x) + log(cos(x)))*|x*\1 + tan (x)/ - ------ + tan(x)| - ---------------------------------------------------------------
\ cos(x) / \ cos(x) / cos(x*tan(x) + log(cos(x)))
$$\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 1\right) \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right) - \frac{\left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right) \sin{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}}{\cos{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}} + \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right) \tan{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}$$
Segunda derivada
[src]
/ 2 \
2 | 2 sin (x) / 2 \ |
/ / 2 \ sin(x) \ 2 |1 + 2*tan (x) - ------- + 2*x*\1 + tan (x)/*tan(x)|*sin(x*tan(x) + log(cos(x)))
2 / 2 \ 2 / 2 \ |x*\1 + tan (x)/ - ------ + tan(x)| *sin (x*tan(x) + log(cos(x))) | 2 | 2
/ / 2 \ sin(x) \ | 2 sin (x) / 2 \ | / / 2 \ sin(x) \ / 2 \ / 2 \ | 2 sin (x) / 2 \ | \ cos(x) / \ cos (x) / / / 2 \ sin(x) \ / 2 \
- |x*\1 + tan (x)/ - ------ + tan(x)| + |1 + 2*tan (x) - ------- + 2*x*\1 + tan (x)/*tan(x)|*tan(x*tan(x) + log(cos(x))) + 2*|x*\1 + tan (x)/ - ------ + tan(x)| *\1 + tan (x*tan(x) + log(cos(x)))/ + \1 + tan (x*tan(x) + log(cos(x)))/*(x*tan(x) + log(cos(x)))*|1 + 2*tan (x) - ------- + 2*x*\1 + tan (x)/*tan(x)| - ----------------------------------------------------------------- - -------------------------------------------------------------------------------- + 2*|x*\1 + tan (x)/ - ------ + tan(x)| *\1 + tan (x*tan(x) + log(cos(x)))/*(x*tan(x) + log(cos(x)))*tan(x*tan(x) + log(cos(x)))
\ cos(x) / | 2 | \ cos(x) / | 2 | 2 cos(x*tan(x) + log(cos(x))) \ cos(x) /
\ cos (x) / \ cos (x) / cos (x*tan(x) + log(cos(x)))
$$2 \left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 1\right) \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right)^{2} \tan{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + \left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 1\right) \left(2 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2 \tan^{2}{\left(x \right)} + 1\right) + 2 \left(\tan^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 1\right) \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right)^{2} - \frac{\left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right)^{2} \sin^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}}{\cos^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}} - \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right)^{2} - \frac{\left(2 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2 \tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}}{\cos{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}} + \left(2 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2 \tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}$$
Tercera derivada
[src]
/ 2 3 \ / 2 \
3 3 | / 2 \ sin(x) sin (x) / 2 \ 2 / 2 \| 2 / / 2 \ sin(x) \ | 2 sin (x) / 2 \ |
/ / 2 \ sin(x) \ / / 2 \ sin(x) \ 3 2*|x*\1 + tan (x)/ - ------ - ------- + 3*\1 + tan (x)/*tan(x) + 2*x*tan (x)*\1 + tan (x)/|*sin(x*tan(x) + log(cos(x))) 3*sin (x*tan(x) + log(cos(x)))*|x*\1 + tan (x)/ - ------ + tan(x)|*|1 + 2*tan (x) - ------- + 2*x*\1 + tan (x)/*tan(x)|
/ 2 \ / 2 3 \ 2*|x*\1 + tan (x)/ - ------ + tan(x)| *sin(x*tan(x) + log(cos(x))) 2*|x*\1 + tan (x)/ - ------ + tan(x)| *sin (x*tan(x) + log(cos(x))) | cos(x) 3 | 2 3 / 2 3 \ 3 / 2 \ \ cos(x) / | 2 | 3 / 2 \
/ / 2 \ sin(x) \ | 2 sin (x) / 2 \ | | / 2 \ sin(x) sin (x) / 2 \ 2 / 2 \| \ cos(x) / \ cos(x) / \ cos (x) / / 2 \ / / 2 \ sin(x) \ / 2 \ | / 2 \ sin(x) sin (x) / 2 \ 2 / 2 \| / / 2 \ sin(x) \ / 2 \ / 2 \ / / 2 \ sin(x) \ | 2 sin (x) / 2 \ | \ cos (x) / / / 2 \ sin(x) \ 2 / 2 \ / 2 \ / / 2 \ sin(x) \ | 2 sin (x) / 2 \ |
- 3*|x*\1 + tan (x)/ - ------ + tan(x)|*|1 + 2*tan (x) - ------- + 2*x*\1 + tan (x)/*tan(x)| + 2*|x*\1 + tan (x)/ - ------ - ------- + 3*\1 + tan (x)/*tan(x) + 2*x*tan (x)*\1 + tan (x)/|*tan(x*tan(x) + log(cos(x))) - ------------------------------------------------------------------ - ------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------ + 2*\1 + tan (x*tan(x) + log(cos(x)))/ *|x*\1 + tan (x)/ - ------ + tan(x)| *(x*tan(x) + log(cos(x))) + 2*\1 + tan (x*tan(x) + log(cos(x)))/*(x*tan(x) + log(cos(x)))*|x*\1 + tan (x)/ - ------ - ------- + 3*\1 + tan (x)/*tan(x) + 2*x*tan (x)*\1 + tan (x)/| + 6*|x*\1 + tan (x)/ - ------ + tan(x)| *\1 + tan (x*tan(x) + log(cos(x)))/*tan(x*tan(x) + log(cos(x))) + 6*\1 + tan (x*tan(x) + log(cos(x)))/*|x*\1 + tan (x)/ - ------ + tan(x)|*|1 + 2*tan (x) - ------- + 2*x*\1 + tan (x)/*tan(x)| - ----------------------------------------------------------------------------------------------------------------------- + 4*|x*\1 + tan (x)/ - ------ + tan(x)| *tan (x*tan(x) + log(cos(x)))*\1 + tan (x*tan(x) + log(cos(x)))/*(x*tan(x) + log(cos(x))) + 6*\1 + tan (x*tan(x) + log(cos(x)))/*(x*tan(x) + log(cos(x)))*|x*\1 + tan (x)/ - ------ + tan(x)|*|1 + 2*tan (x) - ------- + 2*x*\1 + tan (x)/*tan(x)|*tan(x*tan(x) + log(cos(x)))
\ cos(x) / | 2 | | cos(x) 3 | cos(x*tan(x) + log(cos(x))) 3 cos(x*tan(x) + log(cos(x))) \ cos(x) / | cos(x) 3 | \ cos(x) / \ cos(x) / | 2 | 2 \ cos(x) / \ cos(x) / | 2 |
\ cos (x) / \ cos (x) / cos (x*tan(x) + log(cos(x))) \ cos (x) / \ cos (x) / cos (x*tan(x) + log(cos(x))) \ cos (x) /
$$2 \left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 1\right)^{2} \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right)^{3} + 4 \left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 1\right) \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right)^{3} \tan^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 6 \left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 1\right) \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right) \left(2 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2 \tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 2 \left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 1\right) \left(x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 2 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 3 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{\sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) + 6 \left(\tan^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 1\right) \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right)^{3} \tan{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 6 \left(\tan^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)} + 1\right) \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right) \left(2 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2 \tan^{2}{\left(x \right)} + 1\right) - \frac{2 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right)^{3} \sin^{3}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}}{\cos^{3}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}} - \frac{2 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right)^{3} \sin{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}}{\cos{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}} - \frac{3 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right) \left(2 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2 \tan^{2}{\left(x \right)} + 1\right) \sin^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}}{\cos^{2}{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}} - 3 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \tan{\left(x \right)}\right) \left(2 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2 \tan^{2}{\left(x \right)} + 1\right) - \frac{2 \left(x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 2 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 3 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{\sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) \sin{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}}{\cos{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}} + 2 \left(x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 2 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 3 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{\sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) \tan{\left(x \tan{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \right)}$$
Gráfico