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 tan(x/2)
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Derivada de x+4
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Derivada de x^2*sqrt(x)
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Derivada de sin(x)*cos(x)
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Expresiones idénticas
- y=2x^cos(6x)*arctg5x^ tres
- y es igual a 2x en el grado coseno de (6x) multiplicar por arctg5x al cubo
- y es igual a 2x en el grado coseno de (6x) multiplicar por arctg5x en el grado tres
- y=2xcos(6x)*arctg5x3
- y=2xcos6x*arctg5x3
- y=2x^cos(6x)*arctg5x³
- y=2x en el grado cos(6x)*arctg5x en el grado 3
- y=2x^cos(6x)arctg5x^3
- y=2xcos(6x)arctg5x3
- y=2xcos6xarctg5x3
- y=2x^cos6xarctg5x^3
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Expresiones con funciones
- Coseno cos
- cos(sqrt(x))
- cos(x+2)
- cos(x)-sin(x)
- cosxsinx
- cos(x/2)
Derivada de y=2x^cos(6x)*arctg5x^3
Solución
Ha introducido
[src]
cos(6*x) 3 2*x *atan (5*x)
$$2 x^{\cos{\left(6 x \right)}} \operatorname{atan}^{3}{\left(5 x \right)}$$
(2*x^cos(6*x))*atan(5*x)^3
Primera derivada
[src]
cos(6*x) 2
cos(6*x) 3 /cos(6*x) \ 30*x *atan (5*x)
2*x *atan (5*x)*|-------- - 6*log(x)*sin(6*x)| + -----------------------
\ x / 2
1 + 25*x
$$2 x^{\cos{\left(6 x \right)}} \left(- 6 \log{\left(x \right)} \sin{\left(6 x \right)} + \frac{\cos{\left(6 x \right)}}{x}\right) \operatorname{atan}^{3}{\left(5 x \right)} + \frac{30 x^{\cos{\left(6 x \right)}} \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1}$$
Segunda derivada
[src]
/ / cos(6*x) \ \
| / 2 \ 30*|- -------- + 6*log(x)*sin(6*x)|*atan(5*x)|
cos(6*x) | 2 | / cos(6*x) \ cos(6*x) 12*sin(6*x) | 150*(-1 + 5*x*atan(5*x)) \ x / |
-2*x *|atan (5*x)*|- |- -------- + 6*log(x)*sin(6*x)| + -------- + ----------- + 36*cos(6*x)*log(x)| + ------------------------ + ---------------------------------------------|*atan(5*x)
| | \ x / 2 x | 2 2 |
| \ x / / 2\ 1 + 25*x |
\ \1 + 25*x / /
$$- 2 x^{\cos{\left(6 x \right)}} \left(\left(- \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right)^{2} + 36 \log{\left(x \right)} \cos{\left(6 x \right)} + \frac{12 \sin{\left(6 x \right)}}{x} + \frac{\cos{\left(6 x \right)}}{x^{2}}\right) \operatorname{atan}^{2}{\left(5 x \right)} + \frac{30 \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right) \operatorname{atan}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{150 \left(5 x \operatorname{atan}{\left(5 x \right)} - 1\right)}{\left(25 x^{2} + 1\right)^{2}}\right) \operatorname{atan}{\left(5 x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ / 2 \ \
| | 1 2 30*x*atan(5*x) 100*x *atan (5*x)| 2 | / cos(6*x) \ cos(6*x) 12*sin(6*x) | |
| 750*|--------- - atan (5*x) - -------------- + -----------------| 45*atan (5*x)*|- |- -------- + 6*log(x)*sin(6*x)| + -------- + ----------- + 36*cos(6*x)*log(x)| / cos(6*x) \ |
| / 3 \ | 2 2 2 | | \ x / 2 x | 450*(-1 + 5*x*atan(5*x))*|- -------- + 6*log(x)*sin(6*x)|*atan(5*x)|
cos(6*x) | 3 | / cos(6*x) \ 108*cos(6*x) 2*cos(6*x) / cos(6*x) \ /cos(6*x) 12*sin(6*x) \ 18*sin(6*x) | \1 + 25*x 1 + 25*x 1 + 25*x / \ x / \ x / |
2*x *|atan (5*x)*|- |- -------- + 6*log(x)*sin(6*x)| - ------------ + ---------- + 3*|- -------- + 6*log(x)*sin(6*x)|*|-------- + ----------- + 36*cos(6*x)*log(x)| + ----------- + 216*log(x)*sin(6*x)| + ----------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------|
| | \ x / x 3 \ x / | 2 x | 2 | 2 2 2 |
| \ x \ x / x / / 2\ 1 + 25*x / 2\ |
\ \1 + 25*x / \1 + 25*x / /
$$2 x^{\cos{\left(6 x \right)}} \left(\left(- \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right)^{3} + 3 \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right) \left(36 \log{\left(x \right)} \cos{\left(6 x \right)} + \frac{12 \sin{\left(6 x \right)}}{x} + \frac{\cos{\left(6 x \right)}}{x^{2}}\right) + 216 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{108 \cos{\left(6 x \right)}}{x} + \frac{18 \sin{\left(6 x \right)}}{x^{2}} + \frac{2 \cos{\left(6 x \right)}}{x^{3}}\right) \operatorname{atan}^{3}{\left(5 x \right)} - \frac{45 \left(- \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right)^{2} + 36 \log{\left(x \right)} \cos{\left(6 x \right)} + \frac{12 \sin{\left(6 x \right)}}{x} + \frac{\cos{\left(6 x \right)}}{x^{2}}\right) \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{450 \left(5 x \operatorname{atan}{\left(5 x \right)} - 1\right) \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right) \operatorname{atan}{\left(5 x \right)}}{\left(25 x^{2} + 1\right)^{2}} + \frac{750 \left(\frac{100 x^{2} \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1} - \frac{30 x \operatorname{atan}{\left(5 x \right)}}{25 x^{2} + 1} - \operatorname{atan}^{2}{\left(5 x \right)} + \frac{1}{25 x^{2} + 1}\right)}{\left(25 x^{2} + 1\right)^{2}}\right)$$
Gráfico