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- Derivada de una función implícitamente dada
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- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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- Derivada de:
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Derivada de -2*y
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Derivada de 3^2*x
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Derivada de 2*x+8/x
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Derivada de -1/y
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Expresiones idénticas
- x((x- uno)(x+ dos)^(dos))^(uno / tres)/((x- uno)(x+ dos))
- x((x menos 1)(x más 2) en el grado (2)) en el grado (1 dividir por 3) dividir por ((x menos 1)(x más 2))
- x((x menos uno)(x más dos) en el grado (dos)) en el grado (uno dividir por tres) dividir por ((x menos uno)(x más dos))
- x((x-1)(x+2)(2))(1/3)/((x-1)(x+2))
- xx-1x+221/3/x-1x+2
- xx-1x+2^2^1/3/x-1x+2
- x((x-1)(x+2)^(2))^(1 dividir por 3) dividir por ((x-1)(x+2))
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Expresiones semejantes
- x((x-1)(x+2)^(2))^(1/3)/((x+1)(x+2))
- x((x+1)(x+2)^(2))^(1/3)/((x-1)(x+2))
- x((x-1)(x+2)^(2))^(1/3)/((x-1)(x-2))
- x((x-1)(x-2)^(2))^(1/3)/((x-1)(x+2))
Derivada de x((x-1)(x+2)^(2))^(1/3)/((x-1)(x+2))
Solución
Ha introducido
[src]
__________________
3 / 2
x*\/ (x - 1)*(x + 2)
-----------------------
(x - 1)*(x + 2)
$$\frac{x \sqrt[3]{\left(x - 1\right) \left(x + 2\right)^{2}}}{\left(x - 1\right) \left(x + 2\right)}$$
(x*((x - 1)*(x + 2)^2)^(1/3))/(((x - 1)*(x + 2)))
Primera derivada
[src]
/ / 2 \\
| 2/3 |(x + 2) (4 + 2*x)*(x - 1)||
| __________________ x*|x + 2| *|-------- + -----------------|| 3 _______ 2/3
1 |3 / 2 \ 3 3 /| x*\/ x - 1 *|x + 2| *(-1 - 2*x)
---------------*|\/ (x - 1)*(x + 2) + -------------------------------------------| + ---------------------------------
(x - 1)*(x + 2) | 2/3 2 | 2 2
\ (x - 1) *(x + 2) / (x - 1) *(x + 2)
$$\frac{x \sqrt[3]{x - 1} \left|{x + 2}\right|^{\frac{2}{3}} \left(- 2 x - 1\right)}{\left(x - 1\right)^{2} \left(x + 2\right)^{2}} + \frac{1}{\left(x - 1\right) \left(x + 2\right)} \left(\frac{x \left(\frac{\left(x - 1\right) \left(2 x + 4\right)}{3} + \frac{\left(x + 2\right)^{2}}{3}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)^{2}} + \sqrt[3]{\left(x - 1\right) \left(x + 2\right)^{2}}\right)$$
Segunda derivada
[src]
/ / 2/3 3 ________ \ \
| | |2 + x| 2*\/ -1 + x *sign(2 + x)| |
| x*|----------- + ------------------------| |
| 2/3 | 2/3 3 _________ | 2/3 2/3 2/3 | / 2 \
|6*|2 + x| \(-1 + x) \/ |2 + x| / 3*x*|2 + x| 6*x*|2 + x| 6*|2 + x| *(1 + x)| 2/3 |3 ________ x |
x*|------------ + ------------------------------------------ - -------------- - ------------------- + --------------------| 2/3 / 1 + 2*x 1 + 2*x / 1 1 \\ 2*|2 + x| *(1 + 2*x)*|\/ -1 + x + -------------------|
| 2/3 -1 + x 5/3 2/3 2/3 | x*|2 + x| *|-2 + ------- + ------- + (1 + 2*x)*|------ + -----|| | 2/3 |
\(-1 + x) (-1 + x) (-1 + x) *(2 + x) (-1 + x) *(2 + x) / \ -1 + x 2 + x \-1 + x 2 + x// \ (-1 + x) *(2 + x)/
--------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------ - ---------------------------------------------------------
3*(-1 + x) 5/3 2
(-1 + x) (-1 + x)
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
(2 + x)
$$\frac{\frac{x \left(\frac{x \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{x - 1} - \frac{6 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} - \frac{3 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}} + \frac{6 \left(x + 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} + \frac{6 \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{3 \left(x - 1\right)} + \frac{x \left(\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right) - 2 + \frac{2 x + 1}{x + 2} + \frac{2 x + 1}{x - 1}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}} - \frac{2 \left(2 x + 1\right) \left(\frac{x^{2}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} + \sqrt[3]{x - 1}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{2}}}{\left(x + 2\right)^{2}}$$
Tercera derivada
[src]
/ / 2/3 3 ________ \ / 2/3 3 ________ 2 3 ________ \ / 2/3 3 ________ \ / 2/3 3 ________ \ \ / 2/3 3 ________ \ / / 2/3 3 ________ \ \
| | |2 + x| 2*\/ -1 + x *sign(2 + x)| | |2 + x| \/ -1 + x *sign (2 + x) 2*sign(2 + x) 6*\/ -1 + x *DiracDelta(2 + x)| | |2 + x| 2*\/ -1 + x *sign(2 + x)| | |2 + x| 2*\/ -1 + x *sign(2 + x)| | | |2 + x| 2*\/ -1 + x *sign(2 + x)| | | |2 + x| 2*\/ -1 + x *sign(2 + x)| |
| 3*x*|----------- + ------------------------| 2*x*|- ----------- - ----------------------- + ----------------------- + ------------------------------| 6*x*|----------- + ------------------------| 6*(1 + x)*|----------- + ------------------------| | 9*x*|----------- + ------------------------| / / 1 1 \ / 1 1 \ \ | x*|----------- + ------------------------| |
| | 2/3 3 _________ | | 5/3 4/3 2/3 3 _________ 3 _________ | 2/3 2/3 2/3 2/3 | 2/3 3 _________ | | 2/3 3 _________ | 2/3 2/3 | 2/3 | 2/3 3 _________ | 2/3 2/3 | (1 + 2*x)*|------ + -----| (1 + 2*x)*|------ + -----| | / 2 \ | 2/3 | 2/3 3 _________ | 2/3 2/3 2/3 |
| \(-1 + x) \/ |2 + x| / \ (-1 + x) |2 + x| (-1 + x) *\/ |2 + x| \/ |2 + x| / 15*x*|2 + x| 18*|2 + x| 72*|2 + x| *(1 + x) 30*|2 + x| *(1 + x) \(-1 + x) \/ |2 + x| / 6*x*sign(2 + x) \(-1 + x) \/ |2 + x| / 30*x*|2 + x| 54*x*|2 + x| 12*x*sign(2 + x) 12*(1 + x)*sign(2 + x) | 27*x*|2 + x| \(-1 + x) \/ |2 + x| / 54*x*|2 + x| 54*|2 + x| *(1 + x) 2/3 | 8 8 / 1 1 1 \ 3*(1 + 2*x) 3*(1 + 2*x) \-1 + x 2 + x/ \-1 + x 2 + x/ 4*(1 + 2*x) | 2/3 |3 ________ x | / 1 + 2*x 1 + 2*x / 1 1 \\ |6*|2 + x| \(-1 + x) \/ |2 + x| / 3*x*|2 + x| 6*x*|2 + x| 6*|2 + x| *(1 + x)|
x*|- -------------------------------------------- + -------------------------------------------------------------------------------------------------------- + --------------- + ------------------- - --------------------- - --------------------- - -------------------------------------------- - ----------------------- + -------------------------------------------------- + ------------------- + -------------------- - ------------------------------- + -------------------------------| - --------------- + -------------------------------------------- - ------------------- + --------------------- x*|2 + x| *|- ------ - ----- + 2*(1 + 2*x)*|--------- + -------- + ----------------| + ----------- + ----------- + -------------------------- + -------------------------- + ----------------| 3*|2 + x| *|\/ -1 + x + -------------------|*|-2 + ------- + ------- + (1 + 2*x)*|------ + -----|| x*(1 + 2*x)*|------------ + ------------------------------------------ - -------------- - ------------------- + --------------------|
| 2 -1 + x 8/3 2/3 2/3 2 5/3 (-1 + x)*(2 + x) 5/3 3 _________ (-1 + x)*(2 + x) 5/3 2/3 2 2/3 3 _________ 2/3 3 _________| 5/3 -1 + x 2/3 2/3 | -1 + x 2 + x | 2 2 (-1 + x)*(2 + x)| 2 2 -1 + x 2 + x (-1 + x)*(2 + x)| | 2/3 | \ -1 + x 2 + x \-1 + x 2 + x// | 2/3 -1 + x 5/3 2/3 2/3 |
\ (-1 + x) (-1 + x) (-1 + x) *(2 + x) (-1 + x) *(2 + x) (-1 + x) *(2 + x) (-1 + x) *\/ |2 + x| (-1 + x) *(2 + x) (-1 + x) *(2 + x) (-1 + x) *(2 + x)*\/ |2 + x| (-1 + x) *(2 + x)*\/ |2 + x| / (-1 + x) (-1 + x) *(2 + x) (-1 + x) *(2 + x) \ \(-1 + x) (2 + x) / (-1 + x) (2 + x) / \ (-1 + x) *(2 + x)/ \(-1 + x) (-1 + x) (-1 + x) *(2 + x) (-1 + x) *(2 + x) /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------
9*(-1 + x) 5/3 2 2
(-1 + x) (-1 + x) (-1 + x) *(2 + x)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
(2 + x)
$$\frac{- \frac{x \left(2 x + 1\right) \left(\frac{x \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{x - 1} - \frac{6 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} - \frac{3 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}} + \frac{6 \left(x + 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} + \frac{6 \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{\left(x - 1\right)^{2} \left(x + 2\right)} - \frac{x \left(2 \left(2 x + 1\right) \left(\frac{1}{\left(x + 2\right)^{2}} + \frac{1}{\left(x - 1\right) \left(x + 2\right)} + \frac{1}{\left(x - 1\right)^{2}}\right) + \frac{\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right)}{x + 2} - \frac{8}{x + 2} + \frac{3 \left(2 x + 1\right)}{\left(x + 2\right)^{2}} + \frac{\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right)}{x - 1} - \frac{8}{x - 1} + \frac{4 \left(2 x + 1\right)}{\left(x - 1\right) \left(x + 2\right)} + \frac{3 \left(2 x + 1\right)}{\left(x - 1\right)^{2}}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}} + \frac{x \left(\frac{2 x \left(\frac{6 \sqrt[3]{x - 1} \delta\left(x + 2\right)}{\sqrt[3]{\left|{x + 2}\right|}} - \frac{\sqrt[3]{x - 1} \operatorname{sign}^{2}{\left(x + 2 \right)}}{\left|{x + 2}\right|^{\frac{4}{3}}} + \frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left(x - 1\right)^{\frac{2}{3}} \sqrt[3]{\left|{x + 2}\right|}} - \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}}\right)}{x - 1} - \frac{6 x \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{\left(x - 1\right) \left(x + 2\right)} - \frac{3 x \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{\left(x - 1\right)^{2}} - \frac{12 x \operatorname{sign}{\left(x + 2 \right)}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right) \sqrt[3]{\left|{x + 2}\right|}} + \frac{54 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)^{2}} - \frac{6 x \operatorname{sign}{\left(x + 2 \right)}}{\left(x - 1\right)^{\frac{5}{3}} \sqrt[3]{\left|{x + 2}\right|}} + \frac{30 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}} \left(x + 2\right)} + \frac{15 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{8}{3}}} + \frac{6 \left(x + 1\right) \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{\left(x - 1\right) \left(x + 2\right)} + \frac{12 \left(x + 1\right) \operatorname{sign}{\left(x + 2 \right)}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right) \sqrt[3]{\left|{x + 2}\right|}} - \frac{72 \left(x + 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)^{2}} + \frac{18 \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} - \frac{30 \left(x + 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}} \left(x + 2\right)}\right) + \frac{9 x \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{x - 1} - \frac{54 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} - \frac{27 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}} + \frac{54 \left(x + 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)}}{9 \left(x - 1\right)} + \frac{3 \left(\frac{x^{2}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} + \sqrt[3]{x - 1}\right) \left(\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right) - 2 + \frac{2 x + 1}{x + 2} + \frac{2 x + 1}{x - 1}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{2}}}{\left(x + 2\right)^{2}}$$