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 x^(3*x)
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Derivada de x^3*sin(x)
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Derivada de √x
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Derivada de e^x+x^2
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Expresiones idénticas
- y=ln^3arctg(cinco ^xsin5^x)
- y es igual a ln al cubo arctg(5 en el grado x seno de 5 en el grado x)
- y es igual a ln al cubo arctg(cinco en el grado x seno de 5 en el grado x)
- y=ln3arctg(5xsin5x)
- y=ln3arctg5xsin5x
- y=ln³arctg(5^xsin5^x)
- y=ln en el grado 3arctg(5 en el grado xsin5 en el grado x)
- y=ln^3arctg5^xsin5^x
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Expresiones con funciones
- ln
- ln(x+3)^3
- ln(x-1)
- ln(-x)
- ln(1+2x)
- ln((x+1)/(x-1))
Derivada de y=ln^3arctg(5^xsin5^x)
Solución
Ha introducido
[src]
3 / x x \ log (x)*atan\5 *sin (5)/
$$\log{\left(x \right)}^{3} \operatorname{atan}{\left(5^{x} \sin^{x}{\left(5 \right)} \right)}$$
log(x)^3*atan(5^x*sin(5)^x)
Primera derivada
[src]
3 / x x x x \ 2 / x x \
log (x)*\5 *sin (5)*(pi*I + log(-sin(5))) + 5 *sin (5)*log(5)/ 3*log (x)*atan\5 *sin (5)/
-------------------------------------------------------------- + --------------------------
2*x 2*x x
1 + 5 *sin (5)
$$\frac{\left(5^{x} \log{\left(5 \right)} \sin^{x}{\left(5 \right)} + 5^{x} \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right) \sin^{x}{\left(5 \right)}\right) \log{\left(x \right)}^{3}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \frac{3 \log{\left(x \right)}^{2} \operatorname{atan}{\left(5^{x} \sin^{x}{\left(5 \right)} \right)}}{x}$$
Segunda derivada
[src]
/ / 2*x 2 2*x \ \ | x 2 x | 2 2 2*5 *(pi*I + log(5) + log(-sin(5))) *sin (5)| | | 5 *log (x)*sin (5)*|(pi*I + log(-sin(5))) + log (5) + 2*(pi*I + log(-sin(5)))*log(5) - ------------------------------------------------| | | / x x \ | 2*x 2*x | x x | | 3*(-2 + log(x))*atan\5 *sin (5)/ \ 1 + 5 *sin (5) / 6*5 *sin (5)*(pi*I + log(5) + log(-sin(5)))*log(x)| |- -------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------|*log(x) | 2 2*x 2*x / 2*x 2*x \ | \ x 1 + 5 *sin (5) x*\1 + 5 *sin (5)/ /
$$\left(\frac{5^{x} \left(- \frac{2 \cdot 5^{2 x} \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right)^{2} \sin^{2 x}{\left(5 \right)}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \log{\left(5 \right)}^{2} + \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right)^{2} + 2 \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right) \log{\left(5 \right)}\right) \log{\left(x \right)}^{2} \sin^{x}{\left(5 \right)}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \frac{6 \cdot 5^{x} \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right) \log{\left(x \right)} \sin^{x}{\left(5 \right)}}{x \left(5^{2 x} \sin^{2 x}{\left(5 \right)} + 1\right)} - \frac{3 \left(\log{\left(x \right)} - 2\right) \operatorname{atan}{\left(5^{x} \sin^{x}{\left(5 \right)} \right)}}{x^{2}}\right) \log{\left(x \right)}$$
Tercera derivada
[src]
/ 4*x 3 4*x 2*x 2*x / 2 2 \ \
x 3 x | 3 3 2 2 8*5 *(pi*I + log(5) + log(-sin(5))) *sin (5) 8*5 *sin (5)*\(pi*I + log(-sin(5))) + log (5) + 2*(pi*I + log(-sin(5)))*log(5)/*(pi*I + log(5) + log(-sin(5)))| / 2*x 2 2*x \
5 *log (x)*sin (5)*|(pi*I + log(-sin(5))) + log (5) + 3*(pi*I + log(-sin(5))) *log(5) + 3*log (5)*(pi*I + log(-sin(5))) + ------------------------------------------------ - -------------------------------------------------------------------------------------------------------------------| x 2 x | 2 2 2*5 *(pi*I + log(5) + log(-sin(5))) *sin (5)|
| 2 2*x 2*x | 9*5 *log (x)*sin (5)*|(pi*I + log(-sin(5))) + log (5) + 2*(pi*I + log(-sin(5)))*log(5) - ------------------------------------------------|
/ 2 \ / x x \ | / 2*x 2*x \ 1 + 5 *sin (5) | | 2*x 2*x | x x
6*\1 + log (x) - 3*log(x)/*atan\5 *sin (5)/ \ \1 + 5 *sin (5)/ / \ 1 + 5 *sin (5) / 9*5 *sin (5)*(-2 + log(x))*(pi*I + log(5) + log(-sin(5)))*log(x)
------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------
3 2*x 2*x / 2*x 2*x \ 2 / 2*x 2*x \
x 1 + 5 *sin (5) x*\1 + 5 *sin (5)/ x *\1 + 5 *sin (5)/
$$\frac{5^{x} \left(\frac{8 \cdot 5^{4 x} \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right)^{3} \sin^{4 x}{\left(5 \right)}}{\left(5^{2 x} \sin^{2 x}{\left(5 \right)} + 1\right)^{2}} - \frac{8 \cdot 5^{2 x} \left(\log{\left(5 \right)}^{2} + \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right)^{2} + 2 \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right) \log{\left(5 \right)}\right) \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right) \sin^{2 x}{\left(5 \right)}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \log{\left(5 \right)}^{3} + \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right)^{3} + 3 \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right)^{2} \log{\left(5 \right)} + 3 \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right) \log{\left(5 \right)}^{2}\right) \log{\left(x \right)}^{3} \sin^{x}{\left(5 \right)}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \frac{9 \cdot 5^{x} \left(- \frac{2 \cdot 5^{2 x} \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right)^{2} \sin^{2 x}{\left(5 \right)}}{5^{2 x} \sin^{2 x}{\left(5 \right)} + 1} + \log{\left(5 \right)}^{2} + \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right)^{2} + 2 \left(\log{\left(- \sin{\left(5 \right)} \right)} + i \pi\right) \log{\left(5 \right)}\right) \log{\left(x \right)}^{2} \sin^{x}{\left(5 \right)}}{x \left(5^{2 x} \sin^{2 x}{\left(5 \right)} + 1\right)} - \frac{9 \cdot 5^{x} \left(\log{\left(x \right)} - 2\right) \left(\log{\left(- \sin{\left(5 \right)} \right)} + \log{\left(5 \right)} + i \pi\right) \log{\left(x \right)} \sin^{x}{\left(5 \right)}}{x^{2} \left(5^{2 x} \sin^{2 x}{\left(5 \right)} + 1\right)} + \frac{6 \left(\log{\left(x \right)}^{2} - 3 \log{\left(x \right)} + 1\right) \operatorname{atan}{\left(5^{x} \sin^{x}{\left(5 \right)} \right)}}{x^{3}}$$
Gráfico