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- Derivada de una función implícitamente dada
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- Derivada de:
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Derivada de x^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de (-2)/x^3
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Expresiones idénticas
- (ctg(x^ tres +(ln((x^ dos + uno)/(uno -x^ dos)))))^(- dos)
- (ctg(x al cubo más (ln((x al cuadrado más 1) dividir por (1 menos x al cuadrado ))))) en el grado ( menos 2)
- (ctg(x en el grado tres más (ln((x en el grado dos más uno) dividir por (uno menos x en el grado dos))))) en el grado ( menos dos)
- (ctg(x3+(ln((x2+1)/(1-x2)))))(-2)
- ctgx3+lnx2+1/1-x2-2
- (ctg(x³+(ln((x²+1)/(1-x²)))))^(-2)
- (ctg(x en el grado 3+(ln((x en el grado 2+1)/(1-x en el grado 2))))) en el grado (-2)
- ctgx^3+lnx^2+1/1-x^2^-2
- (ctg(x^3+(ln((x^2+1) dividir por (1-x^2)))))^(-2)
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Expresiones semejantes
- (ctg(x^3+(ln((x^2+1)/(1+x^2)))))^(-2)
- (ctg(x^3+(ln((x^2-1)/(1-x^2)))))^(-2)
- (ctg(x^3-(ln((x^2+1)/(1-x^2)))))^(-2)
- (ctg(x^3+(ln((x^2+1)/(1-x^2)))))^(2)
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Expresiones con funciones
- ln
- ln(ax)
- ln4x
- ln(3/x)
- ln(3x²)
- ln√(x-1)
Derivada de (ctg(x^3+(ln((x^2+1)/(1-x^2)))))^(-2)
Solución
Ha introducido
[src]
1
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/ / 2 \\
2| 3 |x + 1||
cot |x + log|------||
| | 2||
\ \1 - x //
$$\frac{1}{\cot^{2}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - x^{2}} \right)} \right)}}$$
cot(x^3 + log((x^2 + 1)/(1 - x^2)))^(-2)
Primera derivada
[src]
/ / / 2 \\\
| / 2\ | 2*x 2*x*\x + 1/||
| \1 - x /*|------ + ------------||
| | 2 2 ||
/ / / 2 \\\ | |1 - x / 2\ ||
| 2| 3 |x + 1||| | 2 \ \1 - x / /|
-2*|-1 - cot |x + log|------|||*|3*x + --------------------------------|
| | | 2||| | 2 |
\ \ \1 - x /// \ x + 1 /
--------------------------------------------------------------------------
/ / 2 \\
3| 3 |x + 1||
cot |x + log|------||
| | 2||
\ \1 - x //
$$- \frac{2 \left(3 x^{2} + \frac{\left(1 - x^{2}\right) \left(\frac{2 x}{1 - x^{2}} + \frac{2 x \left(x^{2} + 1\right)}{\left(1 - x^{2}\right)^{2}}\right)}{x^{2} + 1}\right) \left(- \cot^{2}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - x^{2}} \right)} \right)} - 1\right)}{\cot^{3}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - x^{2}} \right)} \right)}}$$
Segunda derivada
[src]
/ / 2 2 2 / 2\ \ \
| | 1 + x 4*x 4*x *\1 + x / / 2\ / 2\| 2 |
| | -1 + ------- + ------- - ------------- 2 | 1 + x | 2 | 1 + x || / / 2\\ |
| | 2 2 2 2*x *|-1 + -------| 2*x *|-1 + -------|| | | 1 + x || |
| 2 | -1 + x -1 + x / 2\ | 2| | 2|| | 2*|1 - -------|| |
| / / 2\\ | \-1 + x / \ -1 + x / \ -1 + x /| | | 2|| / / / / 2\ \\\|
| | | 1 + x || 2*|3*x - -------------------------------------- + ------------------- - -------------------| 2 | \ -1 + x /| | 2| 3 |-\1 + x / ||||
| | 2*|1 - -------|| | 2 2 / 2\ / 2\| 3*x *|3*x + ---------------| *|1 + cot |x + log|----------||||
/ / / / 2\ \\\ | | | 2|| | 1 + x / 2\ \1 + x /*\-1 + x /| | 2 | | | | 2 ||||
| 2| 3 |-\1 + x / ||| | 2 | \ -1 + x /| \ \1 + x / / \ 1 + x / \ \ \ -1 + x ///|
2*|1 + cot |x + log|----------|||*|- 2*x *|3*x + ---------------| + -------------------------------------------------------------------------------------------- + --------------------------------------------------------------|
| | | 2 ||| | | 2 | / / / 2\ \\ / / / 2\ \\ |
\ \ \ -1 + x /// | \ 1 + x / | 3 |-\1 + x / || 2| 3 |-\1 + x / || |
| cot|x + log|----------|| cot |x + log|----------|| |
| | | 2 || | | 2 || |
\ \ \ -1 + x // \ \ -1 + x // /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / / 2\ \\
2| 3 |-\1 + x / ||
cot |x + log|----------||
| | 2 ||
\ \ -1 + x //
$$\frac{2 \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right) \left(\frac{3 x^{2} \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right)^{2} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}} - 2 x^{2} \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right)^{2} + \frac{2 \left(\frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} + 3 x - \frac{\frac{4 x^{2}}{x^{2} - 1} - \frac{4 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}}{x^{2} + 1}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}}\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}}$$
Tercera derivada
[src]
/ / 2 2 2 / 2\\ / 2 2 2 / 2\\ / 2 2 2 / 2\\ / 2 2 2 / 2\ \ / 2 2 2 / 2\ \\
| / 2\ | 1 + x 4*x 4*x *\1 + x /| / 2\ | 1 + x 2*x 2*x *\1 + x /| / 2\ | 1 + x 4*x 4*x *\1 + x /| / 2\ 3 / / 2\\ | 1 + x 4*x 4*x *\1 + x / / 2\ / 2\| 3 / / 2\\ | 1 + x 4*x 4*x *\1 + x / / 2\ / 2\||
| 3 | 1 + x | 4*x*|-1 + ------- + ------- - -------------| | 1 + x | 12*x*|-1 + ------- + ------- - -------------| | 1 + x | 4*x*|-1 + ------- + ------- - -------------| 3 | 1 + x | / / 2\\ | | 1 + x || | -1 + ------- + ------- - ------------- 2 | 1 + x | 2 | 1 + x || / / 2\\ | | 1 + x || | -1 + ------- + ------- - ------------- 2 | 1 + x | 2 | 1 + x |||
| 8*x *|1 - -------| | 2 2 2 | 2*x*|1 - -------| | 2 2 2 | 2*x*|1 - -------| | 2 2 2 | 8*x *|1 - -------| | | 1 + x || | 2*|1 - -------|| | 2 2 2 2*x *|-1 + -------| 2*x *|-1 + -------|| | | 1 + x || | 2*|1 - -------|| | 2 2 2 2*x *|-1 + -------| 2*x *|-1 + -------|||
| | 2| | -1 + x -1 + x / 2\ | | 2| | -1 + x -1 + x / 2\ | | 2| | -1 + x -1 + x / 2\ | | 2| 3 | 2*|1 - -------|| | | 2|| | -1 + x -1 + x / 2\ | 2| | 2|| 2 | 2*|1 - -------|| / / / / 2\ \\\ | | 2|| | -1 + x -1 + x / 2\ | 2| | 2|||
| \ -1 + x / \ \-1 + x / / \ -1 + x / \ \-1 + x / / \ -1 + x / \ \-1 + x / / \ -1 + x / / / 2\\ | | 2|| / / / / 2\ \\\ | \ -1 + x /| | \-1 + x / \ -1 + x / \ -1 + x /| / / / / 2\ \\\ | | 2|| | 2| 3 |-\1 + x / ||| | \ -1 + x /| | \-1 + x / \ -1 + x / \ -1 + x /||
| -3 - ------------------ - -------------------------------------------- + ----------------- - --------------------------------------------- - ------------------ + -------------------------------------------- + ------------------- | | 1 + x || 3 | \ -1 + x /| | 2| 3 |-\1 + x / ||| 6*x*|3*x + ---------------|*|3*x - -------------------------------------- + ------------------- - -------------------| 3 | 2| 3 |-\1 + x / ||| | \ -1 + x /| 9*x*|1 + cot |x + log|----------|||*|3*x + ---------------|*|3*x - -------------------------------------- + ------------------- - -------------------||
| 3 2 2 / 2\ / 2\ / 2\ / 2\ / 2\ / 2\ 2 | 2*|1 - -------|| 8*x *|3*x + ---------------| *|1 + cot |x + log|----------||| | 2 | | 2 2 / 2\ / 2\| 6*x *|1 + cot |x + log|----------||| *|3*x + ---------------| | | | 2 ||| | 2 | | 2 2 / 2\ / 2\||
/ / / / 2\ \\\ | / 2\ / 2\ / 2\ \1 + x /*\-1 + x / \1 + x /*\-1 + x / \1 + x /*\-1 + x / / 2\ / 2\ | | 2|| | 2 | | | | 2 ||| \ 1 + x / | 1 + x / 2\ \1 + x /*\-1 + x /| | | | 2 ||| | 2 | \ \ \ -1 + x /// \ 1 + x / | 1 + x / 2\ \1 + x /*\-1 + x /||
| 2| 3 |-\1 + x / ||| | \1 + x / \1 + x / \1 + x / \1 + x / *\-1 + x / 3 | \ -1 + x /| \ 1 + x / \ \ \ -1 + x /// \ \1 + x / / \ \ \ -1 + x /// \ 1 + x / \ \1 + x / /|
4*|1 + cot |x + log|----------|||*|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + 2*x *|3*x + ---------------| - -------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------|
| | | 2 ||| | / / / 2\ \\ | 2 | / / / 2\ \\ / / / 2\ \\ / / / 2\ \\ / / / 2\ \\ |
\ \ \ -1 + x /// | 2| 3 |-\1 + x / || \ 1 + x / 2| 3 |-\1 + x / || | 3 |-\1 + x / || 4| 3 |-\1 + x / || 3| 3 |-\1 + x / || |
| cot |x + log|----------|| cot |x + log|----------|| cot|x + log|----------|| cot |x + log|----------|| cot |x + log|----------|| |
| | | 2 || | | 2 || | | 2 || | | 2 || | | 2 || |
\ \ \ -1 + x // \ \ -1 + x // \ \ -1 + x // \ \ -1 + x // \ \ -1 + x // /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / / 2\ \\
| 3 |-\1 + x / ||
cot|x + log|----------||
| | 2 ||
\ \ -1 + x //
$$\frac{4 \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right) \left(\frac{6 x^{3} \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right)^{3} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right)^{2}}{\cot^{4}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}} - \frac{8 x^{3} \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right)^{3} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}} + 2 x^{3} \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right)^{3} + \frac{9 x \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right) \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right) \left(\frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} + 3 x - \frac{\frac{4 x^{2}}{x^{2} - 1} - \frac{4 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}}{x^{2} + 1}\right)}{\cot^{3}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}} - \frac{6 x \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right) \left(\frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} + 3 x - \frac{\frac{4 x^{2}}{x^{2} - 1} - \frac{4 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}}{x^{2} + 1}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}} - \frac{- \frac{8 x^{3} \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{3}} + \frac{8 x^{3} \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)^{2}} + \frac{2 x \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 x \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} - \frac{4 x \left(\frac{4 x^{2}}{x^{2} - 1} - \frac{4 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{12 x \left(\frac{2 x^{2}}{x^{2} - 1} - \frac{2 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} + \frac{4 x \left(\frac{4 x^{2}}{x^{2} - 1} - \frac{4 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} - 3}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}}$$
Gráfico