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 (-4)/x^2
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Derivada de 2/x²
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Derivada de -2*y
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Derivada de (3+2x)/(x-5)
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Expresiones idénticas
- y=(ch^ tres)9x*arctg(5x- uno)
- y es igual a (ch al cubo )9x multiplicar por arctg(5x menos 1)
- y es igual a (ch en el grado tres)9x multiplicar por arctg(5x menos uno)
- y=(ch3)9x*arctg(5x-1)
- y=ch39x*arctg5x-1
- y=(ch³)9x*arctg(5x-1)
- y=(ch en el grado 3)9x*arctg(5x-1)
- y=(ch^3)9xarctg(5x-1)
- y=(ch3)9xarctg(5x-1)
- y=ch39xarctg5x-1
- y=ch^39xarctg5x-1
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Expresiones semejantes
- y=(ch^3)9x*arctg(5x+1)
Derivada de y=(ch^3)9x*arctg(5x-1)
Solución
Ha introducido
[src]
3 cosh (x)*9*x*atan(5*x - 1)
$$x 9 \cosh^{3}{\left(x \right)} \operatorname{atan}{\left(5 x - 1 \right)}$$
((cosh(x)^3*9)*x)*atan(5*x - 1)
Primera derivada
[src]
3
/ 3 2 \ 45*x*cosh (x)
\cosh (x)*9 + 27*x*cosh (x)*sinh(x)/*atan(5*x - 1) + --------------
2
1 + (5*x - 1)
$$\frac{45 x \cosh^{3}{\left(x \right)}}{\left(5 x - 1\right)^{2} + 1} + \left(27 x \sinh{\left(x \right)} \cosh^{2}{\left(x \right)} + 9 \cosh^{3}{\left(x \right)}\right) \operatorname{atan}{\left(5 x - 1 \right)}$$
Segunda derivada
[src]
/ 2 \ | / / 2 2 \ \ 10*(3*x*sinh(x) + cosh(x))*cosh(x) 50*x*cosh (x)*(-1 + 5*x)| 9*|3*\x*\cosh (x) + 2*sinh (x)/ + 2*cosh(x)*sinh(x)/*atan(-1 + 5*x) + ---------------------------------- - ------------------------|*cosh(x) | 2 2 | | 1 + (-1 + 5*x) / 2\ | \ \1 + (-1 + 5*x) / /
$$9 \left(- \frac{50 x \left(5 x - 1\right) \cosh^{2}{\left(x \right)}}{\left(\left(5 x - 1\right)^{2} + 1\right)^{2}} + 3 \left(x \left(2 \sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right) + 2 \sinh{\left(x \right)} \cosh{\left(x \right)}\right) \operatorname{atan}{\left(5 x - 1 \right)} + \frac{10 \left(3 x \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \cosh{\left(x \right)}}{\left(5 x - 1\right)^{2} + 1}\right) \cosh{\left(x \right)}$$
Tercera derivada
[src]
/ / 2 \\ | 3 | 4*(-1 + 5*x) || | 250*x*cosh (x)*|-1 + ---------------|| | / / 2 2 \ \ 2 | 2|| | / / 2 2 \ / 2 2 \ \ 45*\x*\cosh (x) + 2*sinh (x)/ + 2*cosh(x)*sinh(x)/*cosh(x) 150*cosh (x)*(-1 + 5*x)*(3*x*sinh(x) + cosh(x)) \ 1 + (-1 + 5*x) /| 9*|3*\3*\cosh (x) + 2*sinh (x)/*cosh(x) + x*\2*sinh (x) + 7*cosh (x)/*sinh(x)/*atan(-1 + 5*x) + ---------------------------------------------------------- - ----------------------------------------------- + -------------------------------------| | 2 2 2 | | 1 + (-1 + 5*x) / 2\ / 2\ | \ \1 + (-1 + 5*x) / \1 + (-1 + 5*x) / /
$$9 \left(\frac{250 x \left(\frac{4 \left(5 x - 1\right)^{2}}{\left(5 x - 1\right)^{2} + 1} - 1\right) \cosh^{3}{\left(x \right)}}{\left(\left(5 x - 1\right)^{2} + 1\right)^{2}} - \frac{150 \left(5 x - 1\right) \left(3 x \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \cosh^{2}{\left(x \right)}}{\left(\left(5 x - 1\right)^{2} + 1\right)^{2}} + \frac{45 \left(x \left(2 \sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right) + 2 \sinh{\left(x \right)} \cosh{\left(x \right)}\right) \cosh{\left(x \right)}}{\left(5 x - 1\right)^{2} + 1} + 3 \left(x \left(2 \sinh^{2}{\left(x \right)} + 7 \cosh^{2}{\left(x \right)}\right) \sinh{\left(x \right)} + 3 \left(2 \sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right) \cosh{\left(x \right)}\right) \operatorname{atan}{\left(5 x - 1 \right)}\right)$$
Gráfico