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- 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
- (ctg(x^ tres +(ln((x^ dos + uno)/(uno - dos x^ dos)))))^(-2)
- (ctg(x al cubo más (ln((x al cuadrado más 1) dividir por (1 menos 2x 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 dos x en el grado dos))))) en el grado ( menos 2)
- (ctg(x3+(ln((x2+1)/(1-2x2)))))(-2)
- ctgx3+lnx2+1/1-2x2-2
- (ctg(x³+(ln((x²+1)/(1-2x²)))))^(-2)
- (ctg(x en el grado 3+(ln((x en el grado 2+1)/(1-2x en el grado 2))))) en el grado (-2)
- ctgx^3+lnx^2+1/1-2x^2^-2
- (ctg(x^3+(ln((x^2+1) dividir por (1-2x^2)))))^(-2)
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Expresiones semejantes
- (ctg(x^3-(ln((x^2+1)/(1-2x^2)))))^(-2)
- (ctg(x^3+(ln((x^2-1)/(1-2x^2)))))^(-2)
- (ctg(x^3+(ln((x^2+1)/(1+2x^2)))))^(-2)
- (ctg(x^3+(ln((x^2+1)/(1-2x^2)))))^(2)
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Expresiones con funciones
- ln
- ln(×)
- ln(x+a)
- ln(e^x-e^a)
- ln^3(3x)
- ln(2/x)
Derivada de (ctg(x^3+(ln((x^2+1)/(1-2x^2)))))^(-2)
Solución
Ha introducido
[src]
1
------------------------
/ / 2 \\
2| 3 | x + 1 ||
cot |x + log|--------||
| | 2||
\ \1 - 2*x //
$$\frac{1}{\cot^{2}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - 2 x^{2}} \right)} \right)}}$$
cot(x^3 + log((x^2 + 1)/(1 - 2*x^2)))^(-2)
Primera derivada
[src]
/ / / 2 \\\
| / 2\ | 2*x 4*x*\x + 1/||
| \1 - 2*x /*|-------- + ------------||
| | 2 2 ||
/ / / 2 \\\ | |1 - 2*x / 2\ ||
| 2| 3 | x + 1 ||| | 2 \ \1 - 2*x / /|
-2*|-1 - cot |x + log|--------|||*|3*x + ------------------------------------|
| | | 2||| | 2 |
\ \ \1 - 2*x /// \ x + 1 /
--------------------------------------------------------------------------------
/ / 2 \\
3| 3 | x + 1 ||
cot |x + log|--------||
| | 2||
\ \1 - 2*x //
$$- \frac{2 \left(3 x^{2} + \frac{\left(1 - 2 x^{2}\right) \left(\frac{2 x}{1 - 2 x^{2}} + \frac{4 x \left(x^{2} + 1\right)}{\left(1 - 2 x^{2}\right)^{2}}\right)}{x^{2} + 1}\right) \left(- \cot^{2}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - 2 x^{2}} \right)} \right)} - 1\right)}{\cot^{3}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - 2 x^{2}} \right)} \right)}}$$
Segunda derivada
[src]
/ / / 2\ 2 2 / 2\ \ \
| | 2*\1 + x / 8*x 16*x *\1 + x / / / 2\\ / / 2\\| 2 |
| | -1 + ---------- + --------- - -------------- 2 | 2*\1 + x /| 2 | 2*\1 + x /|| / / / 2\\\ |
| | 2 2 2 2*x *|-1 + ----------| 4*x *|-1 + ----------|| | | 2*\1 + x /|| |
| 2 | -1 + 2*x -1 + 2*x / 2\ | 2 | | 2 || | 2*|-1 + ----------|| |
| / / / 2\\\ | \-1 + 2*x / \ -1 + 2*x / \ -1 + 2*x /| | | 2 || / / / / 2\ \\\|
| | | 2*\1 + x /|| 2*|3*x - -------------------------------------------- + ---------------------- - ----------------------| 2 | \ -1 + 2*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 + 2*x / | | 2 | | | | 2 ||||
| 2| 3 |-\1 + x / ||| | 2 | \ -1 + 2*x /| \ \1 + x / / \ 1 + x / \ \ \-1 + 2*x ///|
2*|1 + cot |x + log|----------|||*|- 2*x *|3*x - -------------------| + -------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------|
| | | 2 ||| | | 2 | / / / 2\ \\ / / / 2\ \\ |
\ \ \-1 + 2*x /// | \ 1 + x / | 3 |-\1 + x / || 2| 3 |-\1 + x / || |
| cot|x + log|----------|| cot |x + log|----------|| |
| | | 2 || | | 2 || |
\ \ \-1 + 2*x // \ \-1 + 2*x // /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / / 2\ \\
2| 3 |-\1 + x / ||
cot |x + log|----------||
| | 2 ||
\ \-1 + 2*x //
$$\frac{2 \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right) \left(\frac{3 x^{2} \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right)^{2} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}} - 2 x^{2} \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right)^{2} + \frac{2 \left(- \frac{4 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} + \frac{2 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + 3 x - \frac{- \frac{16 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} + \frac{8 x^{2}}{2 x^{2} - 1} + \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1}{x^{2} + 1}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}}\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}}$$
Tercera derivada
[src]
/ / 2 / 2\ 2 / 2\\ / 2 / 2\ 2 / 2\\ / 2 / 2\ 2 / 2\\ / / 2\ 2 2 / 2\ \ / / 2\ 2 2 / 2\ \\
| / / 2\\ | 8*x 2*\1 + x / 16*x *\1 + x /| / / 2\\ | 4*x 2*\1 + x / 8*x *\1 + x /| / / 2\\ | 8*x 2*\1 + x / 16*x *\1 + x /| / / 2\\ 3 / / / 2\\\ | 2*\1 + x / 8*x 16*x *\1 + x / / / 2\\ / / 2\\| 3 / / / 2\\\ | 2*\1 + x / 8*x 16*x *\1 + x / / / 2\\ / / 2\\||
| 3 | 2*\1 + x /| 4*x*|1 - --------- - ---------- + --------------| | 2*\1 + x /| 24*x*|1 - --------- - ---------- + -------------| | 2*\1 + x /| 8*x*|1 - --------- - ---------- + --------------| 3 | 2*\1 + x /| / / / 2\\\ | | 2*\1 + x /|| | -1 + ---------- + --------- - -------------- 2 | 2*\1 + x /| 2 | 2*\1 + x /|| / / / 2\\\ | | 2*\1 + x /|| | -1 + ---------- + --------- - -------------- 2 | 2*\1 + x /| 2 | 2*\1 + x /|||
| 8*x *|-1 + ----------| | 2 2 2 | 2*x*|-1 + ----------| | 2 2 2| 4*x*|-1 + ----------| | 2 2 2 | 16*x *|-1 + ----------| | | 2*\1 + x /|| | 2*|-1 + ----------|| | 2 2 2 2*x *|-1 + ----------| 4*x *|-1 + ----------|| | | 2*\1 + x /|| | 2*|-1 + ----------|| | 2 2 2 2*x *|-1 + ----------| 4*x *|-1 + ----------|||
| | 2 | | -1 + 2*x -1 + 2*x / 2\ | | 2 | | -1 + 2*x -1 + 2*x / 2\ | | 2 | | -1 + 2*x -1 + 2*x / 2\ | | 2 | 3 | 2*|-1 + ----------|| | | 2 || | -1 + 2*x -1 + 2*x / 2\ | 2 | | 2 || 2 | 2*|-1 + ----------|| / / / / 2\ \\\ | | 2 || | -1 + 2*x -1 + 2*x / 2\ | 2 | | 2 |||
| \ -1 + 2*x / \ \-1 + 2*x / / \ -1 + 2*x / \ \-1 + 2*x / / \ -1 + 2*x / \ \-1 + 2*x / / \ -1 + 2*x / / / / 2\\\ | | 2 || / / / / 2\ \\\ | \ -1 + 2*x /| | \-1 + 2*x / \ -1 + 2*x / \ -1 + 2*x /| / / / / 2\ \\\ | | 2 || | 2| 3 |-\1 + x / ||| | \ -1 + 2*x /| | \-1 + 2*x / \ -1 + 2*x / \ -1 + 2*x /||
|3 - ---------------------- - ------------------------------------------------- + --------------------- - ------------------------------------------------- - --------------------- + ------------------------------------------------- + ----------------------- | | 2*\1 + x /|| 3 | \ -1 + 2*x /| | 2| 3 |-\1 + x / ||| 6*x*|3*x - -------------------|*|3*x - -------------------------------------------- + ---------------------- - ----------------------| 3 | 2| 3 |-\1 + x / ||| | \ -1 + 2*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 + 2*x / \1 + x /*\-1 + 2*x / \1 + x /*\-1 + 2*x / / 2\ / 2\ | | 2 || | 2 | | | | 2 ||| \ 1 + x / | 1 + x / 2\ \1 + x /*\-1 + 2*x / | | | | 2 ||| | 2 | \ \ \-1 + 2*x /// \ 1 + x / | 1 + x / 2\ \1 + x /*\-1 + 2*x / ||
| 2| 3 |-\1 + x / ||| | \1 + x / \1 + x / \1 + x / \1 + x / *\-1 + 2*x / 3 | \ -1 + 2*x /| \ 1 + x / \ \ \-1 + 2*x /// \ \1 + x / / \ \ \-1 + 2*x /// \ 1 + x / \ \1 + x / /|
4*|1 + cot |x + log|----------|||*|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 2*x *|3*x - -------------------| - ------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| | | 2 ||| | / / / 2\ \\ | 2 | / / / 2\ \\ / / / 2\ \\ / / / 2\ \\ / / / 2\ \\ |
\ \ \-1 + 2*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 + 2*x // \ \-1 + 2*x // \ \-1 + 2*x // \ \-1 + 2*x // \ \-1 + 2*x // /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / / 2\ \\
| 3 |-\1 + x / ||
cot|x + log|----------||
| | 2 ||
\ \-1 + 2*x //
$$\frac{4 \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right) \left(\frac{6 x^{3} \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right)^{3} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right)^{2}}{\cot^{4}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}} - \frac{8 x^{3} \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right)^{3} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}} + 2 x^{3} \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right)^{3} + \frac{9 x \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right) \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right) \left(- \frac{4 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} + \frac{2 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + 3 x - \frac{- \frac{16 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} + \frac{8 x^{2}}{2 x^{2} - 1} + \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1}{x^{2} + 1}\right)}{\cot^{3}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}} - \frac{6 x \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right) \left(- \frac{4 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} + \frac{2 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + 3 x - \frac{- \frac{16 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} + \frac{8 x^{2}}{2 x^{2} - 1} + \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1}{x^{2} + 1}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}} + \frac{\frac{16 x^{3} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{2} \left(2 x^{2} - 1\right)} - \frac{8 x^{3} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{3}} - \frac{4 x \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} - \frac{24 x \left(\frac{8 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} - \frac{4 x^{2}}{2 x^{2} - 1} - \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} + 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} + \frac{8 x \left(\frac{16 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} - \frac{8 x^{2}}{2 x^{2} - 1} - \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} + 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} + \frac{2 x \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{4 x \left(\frac{16 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} - \frac{8 x^{2}}{2 x^{2} - 1} - \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} + 1\right)}{\left(x^{2} + 1\right)^{2}} + 3}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}}$$
Gráfico