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+3)/(x-2)
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Derivada de (x+4)^2*(x+1)+9
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Derivada de e^(2-x)
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Expresiones idénticas
- y= dos ^cos6x*arctg5x^ tres
- y es igual a 2 en el grado coseno de 6x multiplicar por arctg5x al cubo
- y es igual a dos en el grado coseno de 6x multiplicar por arctg5x en el grado tres
- y=2cos6x*arctg5x3
- y=2^cos6x*arctg5x³
- y=2 en el grado cos6x*arctg5x en el grado 3
- y=2^cos6xarctg5x^3
- y=2cos6xarctg5x3
Derivada de y=2^cos6x*arctg5x^3
Solución
Ha introducido
[src]
cos(6*x) 3 2 *atan (5*x)
$$2^{\cos{\left(6 x \right)}} \operatorname{atan}^{3}{\left(5 x \right)}$$
2^cos(6*x)*atan(5*x)^3
Primera derivada
[src]
cos(6*x) 2
15*2 *atan (5*x) cos(6*x) 3
----------------------- - 6*2 *atan (5*x)*log(2)*sin(6*x)
2
1 + 25*x
$$- 6 \cdot 2^{\cos{\left(6 x \right)}} \log{\left(2 \right)} \sin{\left(6 x \right)} \operatorname{atan}^{3}{\left(5 x \right)} + \frac{15 \cdot 2^{\cos{\left(6 x \right)}} \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1}$$
Segunda derivada
[src]
cos(6*x) / 25*(-1 + 5*x*atan(5*x)) 2 / 2 \ 30*atan(5*x)*log(2)*sin(6*x)\
6*2 *|- ----------------------- + 6*atan (5*x)*\-cos(6*x) + sin (6*x)*log(2)/*log(2) - ----------------------------|*atan(5*x)
| 2 2 |
| / 2\ 1 + 25*x |
\ \1 + 25*x / /
$$6 \cdot 2^{\cos{\left(6 x \right)}} \left(6 \left(\log{\left(2 \right)} \sin^{2}{\left(6 x \right)} - \cos{\left(6 x \right)}\right) \log{\left(2 \right)} \operatorname{atan}^{2}{\left(5 x \right)} - \frac{30 \log{\left(2 \right)} \sin{\left(6 x \right)} \operatorname{atan}{\left(5 x \right)}}{25 x^{2} + 1} - \frac{25 \left(5 x \operatorname{atan}{\left(5 x \right)} - 1\right)}{\left(25 x^{2} + 1\right)^{2}}\right) \operatorname{atan}{\left(5 x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \
| | 1 2 30*x*atan(5*x) 100*x *atan (5*x)| |
|125*|--------- - atan (5*x) - -------------- + -----------------| |
| | 2 2 2 | 2 / 2 \ |
cos(6*x) | \1 + 25*x 1 + 25*x 1 + 25*x / 3 / 2 2 \ 270*atan (5*x)*\-cos(6*x) + sin (6*x)*log(2)/*log(2) 450*(-1 + 5*x*atan(5*x))*atan(5*x)*log(2)*sin(6*x)|
6*2 *|----------------------------------------------------------------- + 36*atan (5*x)*\1 - log (2)*sin (6*x) + 3*cos(6*x)*log(2)/*log(2)*sin(6*x) + ---------------------------------------------------- + --------------------------------------------------|
| 2 2 2 |
| / 2\ 1 + 25*x / 2\ |
\ \1 + 25*x / \1 + 25*x / /
$$6 \cdot 2^{\cos{\left(6 x \right)}} \left(36 \left(- \log{\left(2 \right)}^{2} \sin^{2}{\left(6 x \right)} + 3 \log{\left(2 \right)} \cos{\left(6 x \right)} + 1\right) \log{\left(2 \right)} \sin{\left(6 x \right)} \operatorname{atan}^{3}{\left(5 x \right)} + \frac{270 \left(\log{\left(2 \right)} \sin^{2}{\left(6 x \right)} - \cos{\left(6 x \right)}\right) \log{\left(2 \right)} \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{450 \left(5 x \operatorname{atan}{\left(5 x \right)} - 1\right) \log{\left(2 \right)} \sin{\left(6 x \right)} \operatorname{atan}{\left(5 x \right)}}{\left(25 x^{2} + 1\right)^{2}} + \frac{125 \left(\frac{100 x^{2} \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1} - \frac{30 x \operatorname{atan}{\left(5 x \right)}}{25 x^{2} + 1} - \operatorname{atan}^{2}{\left(5 x \right)} + \frac{1}{25 x^{2} + 1}\right)}{\left(25 x^{2} + 1\right)^{2}}\right)$$
Gráfico