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 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
- y=(cos(2x- cinco))^arctg5x
- y es igual a ( coseno de (2x menos 5)) en el grado arctg5x
- y es igual a ( coseno de (2x menos cinco)) en el grado arctg5x
- y=(cos(2x-5))arctg5x
- y=cos2x-5arctg5x
- y=cos2x-5^arctg5x
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Expresiones semejantes
- y=(cos(2x+5))^arctg5x
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Expresiones con funciones
- Coseno cos
- cos(x)/sin(x)
- cosx/1+sinx
- cos(3*x)^(2)
- cos(y^2)
- cos(x)/(1-sin(x))
Derivada de y=(cos(2x-5))^arctg5x
Solución
Ha introducido
[src]
atan(5*x) cos (2*x - 5)
$$\cos^{\operatorname{atan}{\left(5 x \right)}}{\left(2 x - 5 \right)}$$
cos(2*x - 5)^atan(5*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
atan(5*x) /5*log(cos(2*x - 5)) 2*atan(5*x)*sin(2*x - 5)\
cos (2*x - 5)*|------------------- - ------------------------|
| 2 cos(2*x - 5) |
\ 1 + 25*x /
$$\left(- \frac{2 \sin{\left(2 x - 5 \right)} \operatorname{atan}{\left(5 x \right)}}{\cos{\left(2 x - 5 \right)}} + \frac{5 \log{\left(\cos{\left(2 x - 5 \right)} \right)}}{25 x^{2} + 1}\right) \cos^{\operatorname{atan}{\left(5 x \right)}}{\left(2 x - 5 \right)}$$
Segunda derivada
[src]
/ 2 2 \
atan(5*x) |/ 5*log(cos(-5 + 2*x)) 2*atan(5*x)*sin(-5 + 2*x)\ 250*x*log(cos(-5 + 2*x)) 20*sin(-5 + 2*x) 4*sin (-5 + 2*x)*atan(5*x)|
cos (-5 + 2*x)*||- -------------------- + -------------------------| - 4*atan(5*x) - ------------------------ - ------------------------- - --------------------------|
|| 2 cos(-5 + 2*x) | 2 / 2\ 2 |
|\ 1 + 25*x / / 2\ \1 + 25*x /*cos(-5 + 2*x) cos (-5 + 2*x) |
\ \1 + 25*x / /
$$\left(- \frac{250 x \log{\left(\cos{\left(2 x - 5 \right)} \right)}}{\left(25 x^{2} + 1\right)^{2}} + \left(\frac{2 \sin{\left(2 x - 5 \right)} \operatorname{atan}{\left(5 x \right)}}{\cos{\left(2 x - 5 \right)}} - \frac{5 \log{\left(\cos{\left(2 x - 5 \right)} \right)}}{25 x^{2} + 1}\right)^{2} - \frac{4 \sin^{2}{\left(2 x - 5 \right)} \operatorname{atan}{\left(5 x \right)}}{\cos^{2}{\left(2 x - 5 \right)}} - 4 \operatorname{atan}{\left(5 x \right)} - \frac{20 \sin{\left(2 x - 5 \right)}}{\left(25 x^{2} + 1\right) \cos{\left(2 x - 5 \right)}}\right) \cos^{\operatorname{atan}{\left(5 x \right)}}{\left(2 x - 5 \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 2 3 2 \
atan(5*x) | / 5*log(cos(-5 + 2*x)) 2*atan(5*x)*sin(-5 + 2*x)\ 60 250*log(cos(-5 + 2*x)) / 5*log(cos(-5 + 2*x)) 2*atan(5*x)*sin(-5 + 2*x)\ | 2*sin (-5 + 2*x)*atan(5*x) 10*sin(-5 + 2*x) 125*x*log(cos(-5 + 2*x))| 60*sin (-5 + 2*x) 16*atan(5*x)*sin(-5 + 2*x) 16*sin (-5 + 2*x)*atan(5*x) 25000*x *log(cos(-5 + 2*x)) 1500*x*sin(-5 + 2*x) |
cos (-5 + 2*x)*|- |- -------------------- + -------------------------| - --------- - ---------------------- + 6*|- -------------------- + -------------------------|*|2*atan(5*x) + -------------------------- + ------------------------- + ------------------------| - -------------------------- - -------------------------- - --------------------------- + --------------------------- + --------------------------|
| | 2 cos(-5 + 2*x) | 2 2 | 2 cos(-5 + 2*x) | | 2 / 2\ 2 | / 2\ 2 cos(-5 + 2*x) 3 3 2 |
| \ 1 + 25*x / 1 + 25*x / 2\ \ 1 + 25*x / | cos (-5 + 2*x) \1 + 25*x /*cos(-5 + 2*x) / 2\ | \1 + 25*x /*cos (-5 + 2*x) cos (-5 + 2*x) / 2\ / 2\ |
\ \1 + 25*x / \ \1 + 25*x / / \1 + 25*x / \1 + 25*x / *cos(-5 + 2*x)/
$$\left(\frac{25000 x^{2} \log{\left(\cos{\left(2 x - 5 \right)} \right)}}{\left(25 x^{2} + 1\right)^{3}} + \frac{1500 x \sin{\left(2 x - 5 \right)}}{\left(25 x^{2} + 1\right)^{2} \cos{\left(2 x - 5 \right)}} - \left(\frac{2 \sin{\left(2 x - 5 \right)} \operatorname{atan}{\left(5 x \right)}}{\cos{\left(2 x - 5 \right)}} - \frac{5 \log{\left(\cos{\left(2 x - 5 \right)} \right)}}{25 x^{2} + 1}\right)^{3} + 6 \left(\frac{2 \sin{\left(2 x - 5 \right)} \operatorname{atan}{\left(5 x \right)}}{\cos{\left(2 x - 5 \right)}} - \frac{5 \log{\left(\cos{\left(2 x - 5 \right)} \right)}}{25 x^{2} + 1}\right) \left(\frac{125 x \log{\left(\cos{\left(2 x - 5 \right)} \right)}}{\left(25 x^{2} + 1\right)^{2}} + \frac{2 \sin^{2}{\left(2 x - 5 \right)} \operatorname{atan}{\left(5 x \right)}}{\cos^{2}{\left(2 x - 5 \right)}} + 2 \operatorname{atan}{\left(5 x \right)} + \frac{10 \sin{\left(2 x - 5 \right)}}{\left(25 x^{2} + 1\right) \cos{\left(2 x - 5 \right)}}\right) - \frac{16 \sin^{3}{\left(2 x - 5 \right)} \operatorname{atan}{\left(5 x \right)}}{\cos^{3}{\left(2 x - 5 \right)}} - \frac{16 \sin{\left(2 x - 5 \right)} \operatorname{atan}{\left(5 x \right)}}{\cos{\left(2 x - 5 \right)}} - \frac{60 \sin^{2}{\left(2 x - 5 \right)}}{\left(25 x^{2} + 1\right) \cos^{2}{\left(2 x - 5 \right)}} - \frac{60}{25 x^{2} + 1} - \frac{250 \log{\left(\cos{\left(2 x - 5 \right)} \right)}}{\left(25 x^{2} + 1\right)^{2}}\right) \cos^{\operatorname{atan}{\left(5 x \right)}}{\left(2 x - 5 \right)}$$
Gráfico