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
-
¿Cómo usar?
- Derivada de:
-
Derivada de 2*cos(3*x)
-
Derivada de x^(7/6)
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Derivada de (x^2)/4
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Derivada de t
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Expresiones idénticas
- y=ln^(cinco)x*arctg2x^(tres)
- y es igual a ln en el grado (5)x multiplicar por arctg2x en el grado (3)
- y es igual a ln en el grado (cinco)x multiplicar por arctg2x en el grado (tres)
- y=ln(5)x*arctg2x(3)
- y=ln5x*arctg2x3
- y=ln^(5)xarctg2x^(3)
- y=ln(5)xarctg2x(3)
- y=ln5xarctg2x3
- y=ln^5xarctg2x^3
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Expresiones con funciones
- ln
- ln(x+k)
- ln4x
- ln(3/x)
- ln√(x-1)
- ln(16+9x^2)
Derivada de y=ln^(5)x*arctg2x^(3)
Solución
Ha introducido
[src]
125 log (x*atan(2*x))
$$\log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{125}$$
log(x*atan(2*x))^125
Primera derivada
[src]
124 / 2*x \
125*log (x*atan(2*x))*|-------- + atan(2*x)|
| 2 |
\1 + 4*x /
----------------------------------------------
x*atan(2*x)
$$\frac{125 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{124}}{x \operatorname{atan}{\left(2 x \right)}}$$
Segunda derivada
[src]
/ / 2 \ 2 \
| / 2*x \ | 4*x | / 2*x \ / 2*x \ |
| |-------- + atan(2*x)|*log(x*atan(2*x)) 4*|-1 + --------|*log(x*atan(2*x)) 124*|-------- + atan(2*x)| 2*|-------- + atan(2*x)|*log(x*atan(2*x))|
| | 2 | | 2| | 2 | | 2 | |
123 | \1 + 4*x / \ 1 + 4*x / \1 + 4*x / \1 + 4*x / |
125*log (x*atan(2*x))*|- --------------------------------------- - ---------------------------------- + --------------------------- - -----------------------------------------|
| x 2 x*atan(2*x) / 2\ |
\ 1 + 4*x \1 + 4*x /*atan(2*x) /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x*atan(2*x)
$$\frac{125 \left(- \frac{2 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{4 \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{4 x^{2} + 1} + \frac{124 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right)^{2}}{x \operatorname{atan}{\left(2 x \right)}} - \frac{\left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{x}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{123}}{x \operatorname{atan}{\left(2 x \right)}}$$
Tercera derivada
[src]
/ / 2 \ 3 2 / 2 \ 2 / 2 \ / 2 \ \
| 2 / 2*x \ 2 | 4*x | / 2*x \ / 2*x \ 2 | 4*x | 2 / 2*x \ / 2*x \ 2 / 2*x \ 2 / 2*x \ 2 | 4*x | | 4*x | / 2*x \ |
|log (x*atan(2*x))*|-------- + atan(2*x)| 32*log (x*atan(2*x))*|-1 + --------| 7626*|-------- + atan(2*x)| 186*|-------- + atan(2*x)| *log(x*atan(2*x)) 4*log (x*atan(2*x))*|-1 + --------| 8*log (x*atan(2*x))*|-------- + atan(2*x)| 372*|-------- + atan(2*x)| *log(x*atan(2*x)) 2*log (x*atan(2*x))*|-------- + atan(2*x)| 4*log (x*atan(2*x))*|-------- + atan(2*x)| 8*log (x*atan(2*x))*|-1 + --------| 744*|-1 + --------|*|-------- + atan(2*x)|*log(x*atan(2*x))|
| | 2 | | 2| | 2 | | 2 | | 2| | 2 | | 2 | | 2 | | 2 | | 2| | 2| | 2 | |
122 | \1 + 4*x / \ 1 + 4*x / \1 + 4*x / \1 + 4*x / \ 1 + 4*x / \1 + 4*x / \1 + 4*x / \1 + 4*x / \1 + 4*x / \ 1 + 4*x / \ 1 + 4*x / \1 + 4*x / |
250*log (x*atan(2*x))*|---------------------------------------- + ------------------------------------ + ---------------------------- - -------------------------------------------- + ----------------------------------- + ------------------------------------------ - -------------------------------------------- + ------------------------------------------ + ------------------------------------------ + ----------------------------------- - -----------------------------------------------------------|
| 3 2 3 2 3 2 / 2\ 2 2 / 2\ 2 2 / 2\ 2 2 2 / 2\ |
| x / 2\ x *atan (2*x) x *atan(2*x) x *\1 + 4*x / / 2\ x *\1 + 4*x /*atan (2*x) x *\1 + 4*x /*atan(2*x) / 2\ 2 / 2\ x *\1 + 4*x /*atan(2*x) |
\ \1 + 4*x / \1 + 4*x / *atan(2*x) x*\1 + 4*x / *atan (2*x) x*\1 + 4*x / *atan(2*x) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
atan(2*x)
$$\frac{250 \left(\frac{8 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \frac{32 \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{\left(4 x^{2} + 1\right)^{2}} + \frac{4 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{x \left(4 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(2 x \right)}} + \frac{8 \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{x \left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} - \frac{372 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right)^{2} \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{x^{2} \left(4 x^{2} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)}} - \frac{744 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{x^{2} \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \frac{2 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{x^{2} \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \frac{4 \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{x^{2} \left(4 x^{2} + 1\right)} + \frac{7626 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right)^{3}}{x^{3} \operatorname{atan}^{2}{\left(2 x \right)}} - \frac{186 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right)^{2} \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{x^{3} \operatorname{atan}{\left(2 x \right)}} + \frac{\left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{x^{3}}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{122}}{\operatorname{atan}{\left(2 x \right)}}$$
Gráfico