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^4(3x-7)^5
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Derivada de x⁴+8x²+8
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Derivada de (x^3+e^x)/sqrt(4-9*x^5)
- Derivada de x=3acost-acos3t,y=3asint-asin3tfinddy÷dx
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Expresiones idénticas
- (x*e^x*arctgx)/(ln cinco x)^5
- (x multiplicar por e en el grado x multiplicar por arctgx) dividir por (ln5x) en el grado 5
- (x multiplicar por e en el grado x multiplicar por arctgx) dividir por (ln cinco x) en el grado 5
- (x*ex*arctgx)/(ln5x)5
- x*ex*arctgx/ln5x5
- (x*e^x*arctgx)/(ln5x)⁵
- (xe^xarctgx)/(ln5x)^5
- (xexarctgx)/(ln5x)5
- xexarctgx/ln5x5
- xe^xarctgx/ln5x^5
- (x*e^x*arctgx) dividir por (ln5x)^5
Derivada de (x*e^x*arctgx)/(ln5x)^5
Solución
Ha introducido
[src]
x
x*E *acot(x)
------------
5
log (5*x)
$$\frac{e^{x} x \operatorname{acot}{\left(x \right)}}{\log{\left(5 x \right)}^{5}}$$
((x*E^x)*acot(x))/log(5*x)^5
Primera derivada
[src]
x
/ x x\ x*e
\E + x*e /*acot(x) - ------
2 x
1 + x 5*acot(x)*e
---------------------------- - ------------
5 6
log (5*x) log (5*x)
$$\frac{- \frac{x e^{x}}{x^{2} + 1} + \left(e^{x} + x e^{x}\right) \operatorname{acot}{\left(x \right)}}{\log{\left(5 x \right)}^{5}} - \frac{5 e^{x} \operatorname{acot}{\left(x \right)}}{\log{\left(5 x \right)}^{6}}$$
Segunda derivada
[src]
/ / x \ \
| 10*|------ - (1 + x)*acot(x)| / 6 \ |
| 2 | 2 | 5*|1 + --------|*acot(x)|
| 2*(1 + x) 2*x \1 + x / \ log(5*x)/ | x
|(2 + x)*acot(x) - --------- + --------- + ----------------------------- + ------------------------|*e
| 2 2 x*log(5*x) x*log(5*x) |
| 1 + x / 2\ |
\ \1 + x / /
-------------------------------------------------------------------------------------------------------
5
log (5*x)
$$\frac{\left(\frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{acot}{\left(x \right)} + \frac{5 \left(1 + \frac{6}{\log{\left(5 x \right)}}\right) \operatorname{acot}{\left(x \right)}}{x \log{\left(5 x \right)}} + \frac{10 \left(\frac{x}{x^{2} + 1} - \left(x + 1\right) \operatorname{acot}{\left(x \right)}\right)}{x \log{\left(5 x \right)}}\right) e^{x}}{\log{\left(5 x \right)}^{5}}$$
Tercera derivada
[src]
/ / 2 \ \
| | 2*(1 + x) 2*x | / 2 \ |
| 15*|(2 + x)*acot(x) - --------- + ---------| | 4*x | / 6 \ / x \ / 9 21 \ |
| | 2 2| 2*x*|-1 + ------| 15*|1 + --------|*|------ - (1 + x)*acot(x)| 10*|1 + -------- + ---------|*acot(x)|
| | 1 + x / 2\ | | 2| \ log(5*x)/ | 2 | | log(5*x) 2 | |
| 3*(2 + x) \ \1 + x / / \ 1 + x / 6*x*(1 + x) \1 + x / \ log (5*x)/ | x
|(3 + x)*acot(x) - --------- - -------------------------------------------- - ----------------- + ----------- - -------------------------------------------- - -------------------------------------|*e
| 2 x*log(5*x) 2 2 2 2 |
| 1 + x / 2\ / 2\ x *log(5*x) x *log(5*x) |
\ \1 + x / \1 + x / /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5
log (5*x)
$$\frac{\left(\frac{6 x \left(x + 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(x + 2\right)}{x^{2} + 1} + \left(x + 3\right) \operatorname{acot}{\left(x \right)} - \frac{15 \left(\frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{acot}{\left(x \right)}\right)}{x \log{\left(5 x \right)}} - \frac{15 \left(1 + \frac{6}{\log{\left(5 x \right)}}\right) \left(\frac{x}{x^{2} + 1} - \left(x + 1\right) \operatorname{acot}{\left(x \right)}\right)}{x^{2} \log{\left(5 x \right)}} - \frac{10 \left(1 + \frac{9}{\log{\left(5 x \right)}} + \frac{21}{\log{\left(5 x \right)}^{2}}\right) \operatorname{acot}{\left(x \right)}}{x^{2} \log{\left(5 x \right)}}\right) e^{x}}{\log{\left(5 x \right)}^{5}}$$
Gráfico