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 1/(x+1)^2
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Derivada de x^12
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Derivada de (x+3)/(x-2)
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Derivada de (x^3-4)
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Expresiones idénticas
- y=(cosx^ dos)^(ln(x^ dos - dos *x+ uno))
- y es igual a ( coseno de x al cuadrado ) en el grado (ln(x al cuadrado menos 2 multiplicar por x más 1))
- y es igual a ( coseno de x en el grado dos) en el grado (ln(x en el grado dos menos dos multiplicar por x más uno))
- y=(cosx2)(ln(x2-2*x+1))
- y=cosx2lnx2-2*x+1
- y=(cosx²)^(ln(x²-2*x+1))
- y=(cosx en el grado 2) en el grado (ln(x en el grado 2-2*x+1))
- y=(cosx^2)^(ln(x^2-2x+1))
- y=(cosx2)(ln(x2-2x+1))
- y=cosx2lnx2-2x+1
- y=cosx^2^lnx^2-2x+1
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Expresiones semejantes
- y=(cosx^2)^(ln(x^2-2*x-1))
- y=(cosx^2)^(ln(x^2+2*x+1))
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Expresiones con funciones
- cosx
- cosx/lnx
- ln
- ln(x)+x
- ln(x+4)^11
- ln(x)+1
- ln(2x)/x
- ln|x|
Derivada de y=(cosx^2)^(ln(x^2-2*x+1))
Solución
Ha introducido
[src]
/ 2 \
log\x - 2*x + 1/
2
cos (x)
$$\left(\cos^{2}{\left(x \right)}\right)^{\log{\left(\left(x^{2} - 2 x\right) + 1 \right)}}$$
(cos(x)^2)^log(x^2 - 2*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 \ / / 2 \ / 2 \ \
2*log\x - 2*x + 1/ |(-2 + 2*x)*log\cos (x)/ 2*log\x - 2*x + 1/*sin(x)|
|cos(x)| *|----------------------- - --------------------------|
| 2 cos(x) |
\ x - 2*x + 1 /
$$\left(\frac{\left(2 x - 2\right) \log{\left(\cos^{2}{\left(x \right)} \right)}}{\left(x^{2} - 2 x\right) + 1} - \frac{2 \log{\left(\left(x^{2} - 2 x\right) + 1 \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) \left|{\cos{\left(x \right)}}\right|^{2 \log{\left(\left(x^{2} - 2 x\right) + 1 \right)}}$$
Segunda derivada
[src]
/ 2 \ / / 2 \ / / 2 \ / 2 \ \ / / 2 \ \ 2 / 2 \ 2 / 2 \ \
2*log\1 + x - 2*x/ | / 2 \ log\cos (x)/ |(-1 + x)*log\cos (x)/ log\1 + x - 2*x/*sin(x)| |2*(-1 + x)*log(|cos(x)|) log\1 + x - 2*x/*sign(cos(x))*sin(x)| sin (x)*log\1 + x - 2*x/ 2*(-1 + x) *log\cos (x)/ 4*(-1 + x)*sin(x) |
2*|cos(x)| *|- log\1 + x - 2*x/ + ------------ + 2*|--------------------- - ------------------------|*|------------------------ - -------------------------------------| - ------------------------- - ------------------------ - ---------------------|
| 2 | 2 cos(x) | | 2 |cos(x)| | 2 2 / 2 \ |
| 1 + x - 2*x \ 1 + x - 2*x / \ 1 + x - 2*x / cos (x) / 2 \ \1 + x - 2*x/*cos(x)|
\ \1 + x - 2*x/ /
$$2 \left(- \frac{2 \left(x - 1\right)^{2} \log{\left(\cos^{2}{\left(x \right)} \right)}}{\left(x^{2} - 2 x + 1\right)^{2}} - \frac{4 \left(x - 1\right) \sin{\left(x \right)}}{\left(x^{2} - 2 x + 1\right) \cos{\left(x \right)}} + 2 \left(\frac{\left(x - 1\right) \log{\left(\cos^{2}{\left(x \right)} \right)}}{x^{2} - 2 x + 1} - \frac{\log{\left(x^{2} - 2 x + 1 \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) \left(\frac{2 \left(x - 1\right) \log{\left(\left|{\cos{\left(x \right)}}\right| \right)}}{x^{2} - 2 x + 1} - \frac{\log{\left(x^{2} - 2 x + 1 \right)} \sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\left|{\cos{\left(x \right)}}\right|}\right) - \frac{\log{\left(x^{2} - 2 x + 1 \right)} \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - \log{\left(x^{2} - 2 x + 1 \right)} + \frac{\log{\left(\cos^{2}{\left(x \right)} \right)}}{x^{2} - 2 x + 1}\right) \left|{\cos{\left(x \right)}}\right|^{2 \log{\left(x^{2} - 2 x + 1 \right)}}$$
Tercera derivada
[src]
/ 2 \
/ 2 \ | / / 2 \ / 2 \ \ / 2 / 2 \ 2 2 / 2 \ 2 / 2 \ \ / / 2 \ \ / / 2 \ 2 / 2 \ 2 / 2 \ \ / / 2 \ \ / / 2 \ / 2 \ \ / 2 \ 3 / 2 \ / 2 \ 3 / 2 \ 2 2 |
2*log\1 + x - 2*x/ | |(-1 + x)*log\cos (x)/ log\1 + x - 2*x/*sin(x)| | 2*log(|cos(x)|) 4*(-1 + x) *log(|cos(x)|) cos(x)*log\1 + x - 2*x/*sign(cos(x)) sign (cos(x))*sin (x)*log\1 + x - 2*x/ 2*sin (x)*DiracDelta(cos(x))*log\1 + x - 2*x/ 4*(-1 + x)*sign(cos(x))*sin(x)| 3*(-1 + x) |2*(-1 + x)*log(|cos(x)|) log\1 + x - 2*x/*sign(cos(x))*sin(x)| | log\cos (x)/ sin (x)*log\1 + x - 2*x/ 2*(-1 + x) *log\cos (x)/ 4*(-1 + x)*sin(x) / 2 \| |2*(-1 + x)*log(|cos(x)|) log\1 + x - 2*x/*sign(cos(x))*sin(x)| |(-1 + x)*log\cos (x)/ log\1 + x - 2*x/*sin(x)| log\1 + x - 2*x/*sin(x) sin (x)*log\1 + x - 2*x/ 3*sin(x) 3*(-1 + x)*log\cos (x)/ 4*(-1 + x) *log\cos (x)/ 3*sin (x)*(-1 + x) 6*(-1 + x) *sin(x) |
4*|cos(x)| *|- |--------------------- - ------------------------|*|- --------------- + ------------------------- + ------------------------------------- + --------------------------------------- - ---------------------------------------------- + ------------------------------| - ------------ - 2*|------------------------ - -------------------------------------|*|- ------------ + ------------------------- + ------------------------ + --------------------- + log\1 + x - 2*x/| + 2*|------------------------ - -------------------------------------| *|--------------------- - ------------------------| - ------------------------ - ------------------------- - --------------------- - ----------------------- + ------------------------ - ---------------------- + ----------------------|
| | 2 cos(x) | | 2 2 |cos(x)| 2 |cos(x)| / 2 \ | 2 | 2 |cos(x)| | | 2 2 2 / 2 \ | | 2 |cos(x)| | | 2 cos(x) | cos(x) 3 / 2 \ 2 3 / 2 \ 2 2 |
| \ 1 + x - 2*x / | 1 + x - 2*x / 2 \ cos (x) \1 + x - 2*x/*|cos(x)| | 1 + x - 2*x \ 1 + x - 2*x / | 1 + x - 2*x cos (x) / 2 \ \1 + x - 2*x/*cos(x) | \ 1 + x - 2*x / \ 1 + x - 2*x / cos (x) \1 + x - 2*x/*cos(x) / 2 \ / 2 \ \1 + x - 2*x/*cos (x) / 2 \ |
\ \ \1 + x - 2*x/ / \ \1 + x - 2*x/ / \1 + x - 2*x/ \1 + x - 2*x/ \1 + x - 2*x/ *cos(x)/
$$4 \left(\frac{4 \left(x - 1\right)^{3} \log{\left(\cos^{2}{\left(x \right)} \right)}}{\left(x^{2} - 2 x + 1\right)^{3}} + \frac{6 \left(x - 1\right)^{2} \sin{\left(x \right)}}{\left(x^{2} - 2 x + 1\right)^{2} \cos{\left(x \right)}} - \frac{3 \left(x - 1\right) \sin^{2}{\left(x \right)}}{\left(x^{2} - 2 x + 1\right) \cos^{2}{\left(x \right)}} - \frac{3 \left(x - 1\right)}{x^{2} - 2 x + 1} - \frac{3 \left(x - 1\right) \log{\left(\cos^{2}{\left(x \right)} \right)}}{\left(x^{2} - 2 x + 1\right)^{2}} + 2 \left(\frac{\left(x - 1\right) \log{\left(\cos^{2}{\left(x \right)} \right)}}{x^{2} - 2 x + 1} - \frac{\log{\left(x^{2} - 2 x + 1 \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) \left(\frac{2 \left(x - 1\right) \log{\left(\left|{\cos{\left(x \right)}}\right| \right)}}{x^{2} - 2 x + 1} - \frac{\log{\left(x^{2} - 2 x + 1 \right)} \sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\left|{\cos{\left(x \right)}}\right|}\right)^{2} - \left(\frac{\left(x - 1\right) \log{\left(\cos^{2}{\left(x \right)} \right)}}{x^{2} - 2 x + 1} - \frac{\log{\left(x^{2} - 2 x + 1 \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) \left(\frac{4 \left(x - 1\right)^{2} \log{\left(\left|{\cos{\left(x \right)}}\right| \right)}}{\left(x^{2} - 2 x + 1\right)^{2}} + \frac{4 \left(x - 1\right) \sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\left(x^{2} - 2 x + 1\right) \left|{\cos{\left(x \right)}}\right|} - \frac{2 \log{\left(x^{2} - 2 x + 1 \right)} \sin^{2}{\left(x \right)} \delta\left(\cos{\left(x \right)}\right)}{\left|{\cos{\left(x \right)}}\right|} + \frac{\log{\left(x^{2} - 2 x + 1 \right)} \sin^{2}{\left(x \right)} \operatorname{sign}^{2}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)}} + \frac{\log{\left(x^{2} - 2 x + 1 \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\left|{\cos{\left(x \right)}}\right|} - \frac{2 \log{\left(\left|{\cos{\left(x \right)}}\right| \right)}}{x^{2} - 2 x + 1}\right) - 2 \left(\frac{2 \left(x - 1\right) \log{\left(\left|{\cos{\left(x \right)}}\right| \right)}}{x^{2} - 2 x + 1} - \frac{\log{\left(x^{2} - 2 x + 1 \right)} \sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\left|{\cos{\left(x \right)}}\right|}\right) \left(\frac{2 \left(x - 1\right)^{2} \log{\left(\cos^{2}{\left(x \right)} \right)}}{\left(x^{2} - 2 x + 1\right)^{2}} + \frac{4 \left(x - 1\right) \sin{\left(x \right)}}{\left(x^{2} - 2 x + 1\right) \cos{\left(x \right)}} + \frac{\log{\left(x^{2} - 2 x + 1 \right)} \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \log{\left(x^{2} - 2 x + 1 \right)} - \frac{\log{\left(\cos^{2}{\left(x \right)} \right)}}{x^{2} - 2 x + 1}\right) - \frac{\log{\left(x^{2} - 2 x + 1 \right)} \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{\log{\left(x^{2} - 2 x + 1 \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{3 \sin{\left(x \right)}}{\left(x^{2} - 2 x + 1\right) \cos{\left(x \right)}}\right) \left|{\cos{\left(x \right)}}\right|^{2 \log{\left(x^{2} - 2 x + 1 \right)}}$$