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- Derivada de una función implícitamente dada
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- Derivada de:
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Derivada de 8x²+7x+4
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Derivada de -(853/100)
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Derivada de (7x)
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Derivada de (8)
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Expresiones idénticas
- y=(((x+ uno)^ dos)^(uno / cinco))/(((x- tres)^ dos)*((x- cuatro)^ tres))
- y es igual a (((x más 1) al cuadrado ) en el grado (1 dividir por 5)) dividir por (((x menos 3) al cuadrado ) multiplicar por ((x menos 4) al cubo ))
- y es igual a (((x más uno) en el grado dos) en el grado (uno dividir por cinco)) dividir por (((x menos tres) en el grado dos) multiplicar por ((x menos cuatro) en el grado tres))
- y=(((x+1)2)(1/5))/(((x-3)2)*((x-4)3))
- y=x+121/5/x-32*x-43
- y=(((x+1)²)^(1/5))/(((x-3)²)*((x-4)³))
- y=(((x+1) en el grado 2) en el grado (1/5))/(((x-3) en el grado 2)*((x-4) en el grado 3))
- y=(((x+1)^2)^(1/5))/(((x-3)^2)((x-4)^3))
- y=(((x+1)2)(1/5))/(((x-3)2)((x-4)3))
- y=x+121/5/x-32x-43
- y=x+1^2^1/5/x-3^2x-4^3
- y=(((x+1)^2)^(1 dividir por 5)) dividir por (((x-3)^2)*((x-4)^3))
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Expresiones semejantes
- y=(((x+1)^2)^(1/5))/(((x-3)^2)*((x+4)^3))
- y=(((x-1)^2)^(1/5))/(((x-3)^2)*((x-4)^3))
- y=(((x+1)^2)^(1/5))/(((x+3)^2)*((x-4)^3))
Derivada de y=(((x+1)^2)^(1/5))/(((x-3)^2)*((x-4)^3))
Solución
Ha introducido
[src]
__________
5 / 2
\/ (x + 1)
-----------------
2 3
(x - 3) *(x - 4)
$$\frac{\sqrt[5]{\left(x + 1\right)^{2}}}{\left(x - 4\right)^{3} \left(x - 3\right)^{2}}$$
((x + 1)^2)^(1/5)/(((x - 3)^2*(x - 4)^3))
Primera derivada
[src]
2/5 1 /2 2*x\
|x + 1| *-----------------*|- + ---|
3 2 \5 5 / 2/5 / 3 2 2\
(x - 4) *(x - 3) |x + 1| *\- (x - 4) *(-6 + 2*x) - 3*(x - 4) *(x - 3) /
-------------------------------------- + --------------------------------------------------------
2 6 4
(x + 1) (x - 4) *(x - 3)
$$\frac{\frac{1}{\left(x - 4\right)^{3} \left(x - 3\right)^{2}} \left(\frac{2 x}{5} + \frac{2}{5}\right) \left|{x + 1}\right|^{\frac{2}{5}}}{\left(x + 1\right)^{2}} + \frac{\left(- \left(x - 4\right)^{3} \left(2 x - 6\right) - 3 \left(x - 4\right)^{2} \left(x - 3\right)^{2}\right) \left|{x + 1}\right|^{\frac{2}{5}}}{\left(x - 4\right)^{6} \left(x - 3\right)^{4}}$$
Segunda derivada
[src]
/ 2/5 \
| 5*|1 + x| 2*sign(1 + x)| / / 2 2 \\
2*|- ------------ + -------------| 2/5 | / 2 3 \ 2*(-17 + 5*x) 3*(-17 + 5*x) 2*\(-4 + x) + 3*(-3 + x) + 6*(-4 + x)*(-3 + x)/|
| 1 + x 3/5 | |1 + x| *|(-17 + 5*x)*|------ + ------| + ------------- + ------------- - -------------------------------------------------| 2/5
\ |1 + x| / \ \-3 + x -4 + x/ -3 + x -4 + x (-4 + x)*(-3 + x) / 4*|1 + x| *(-17 + 5*x)
---------------------------------- + ------------------------------------------------------------------------------------------------------------------------------ - ---------------------------
25*(1 + x) (-4 + x)*(-3 + x) 5*(1 + x)*(-4 + x)*(-3 + x)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 2
(-4 + x) *(-3 + x)
$$\frac{\frac{2 \left(\frac{2 \operatorname{sign}{\left(x + 1 \right)}}{\left|{x + 1}\right|^{\frac{3}{5}}} - \frac{5 \left|{x + 1}\right|^{\frac{2}{5}}}{x + 1}\right)}{25 \left(x + 1\right)} + \frac{\left(\left(5 x - 17\right) \left(\frac{2}{x - 3} + \frac{3}{x - 4}\right) + \frac{2 \left(5 x - 17\right)}{x - 3} + \frac{3 \left(5 x - 17\right)}{x - 4} - \frac{2 \left(\left(x - 4\right)^{2} + 6 \left(x - 4\right) \left(x - 3\right) + 3 \left(x - 3\right)^{2}\right)}{\left(x - 4\right) \left(x - 3\right)}\right) \left|{x + 1}\right|^{\frac{2}{5}}}{\left(x - 4\right) \left(x - 3\right)} - \frac{4 \left(5 x - 17\right) \left|{x + 1}\right|^{\frac{2}{5}}}{5 \left(x - 4\right) \left(x - 3\right) \left(x + 1\right)}}{\left(x - 4\right)^{3} \left(x - 3\right)^{2}}$$
Tercera derivada
[src]
/ / 2 3 \ / 2 3 \ / 2 3 \ / 2 2 \\
/ 2 2/5 \ | / 2 2 \ / 2 2 \ 2*(-17 + 5*x)*|------ + ------| 3*(-17 + 5*x)*|------ + ------| / 2 2 \ 2*|------ + ------|*\(-4 + x) + 3*(-3 + x) + 6*(-4 + x)*(-3 + x)/| / 2/5 \
| 3*sign (1 + x) 10*DiracDelta(1 + x) 25*|1 + x| 10*sign(1 + x) | 2/5 | / 1 2 2 \ 10*(-17 + 5*x) 21*(-17 + 5*x) 18*\(-4 + x) + 3*(-3 + x) + 6*(-4 + x)*(-3 + x)/ 12*\(-4 + x) + 3*(-3 + x) + 6*(-4 + x)*(-3 + x)/ \-3 + x -4 + x/ \-3 + x -4 + x/ 6*\(-3 + x) + 3*(-4 + x) + 6*(-4 + x)*(-3 + x)/ 24*(-17 + 5*x) \-3 + x -4 + x/ | | 5*|1 + x| 2*sign(1 + x)| / / 2 2 \\
4*|- -------------- + -------------------- + ------------- - ------------------| |1 + x| *|6*(-17 + 5*x)*|--------- + --------- + -----------------| + -------------- + -------------- - -------------------------------------------------- - -------------------------------------------------- + ------------------------------- + ------------------------------- + ------------------------------------------------- + ----------------- - -------------------------------------------------------------------| 6*(-17 + 5*x)*|- ------------ + -------------| 2/5 | / 2 3 \ 2*(-17 + 5*x) 3*(-17 + 5*x) 2*\(-4 + x) + 3*(-3 + x) + 6*(-4 + x)*(-3 + x)/|
| 8/5 3/5 2 3/5| | | 2 2 (-4 + x)*(-3 + x)| 2 2 2 2 -3 + x -4 + x 2 (-4 + x)*(-3 + x) (-4 + x)*(-3 + x) | | 1 + x 3/5 | 6*|1 + x| *|(-17 + 5*x)*|------ + ------| + ------------- + ------------- - -------------------------------------------------|
\ |1 + x| |1 + x| (1 + x) (1 + x)*|1 + x| / \ \(-3 + x) (-4 + x) / (-3 + x) (-4 + x) (-4 + x) *(-3 + x) (-4 + x)*(-3 + x) (-4 + x) *(-3 + x) / \ |1 + x| / \ \-3 + x -4 + x/ -3 + x -4 + x (-4 + x)*(-3 + x) /
-------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ---------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------
125*(1 + x) (-4 + x)*(-3 + x) 25*(1 + x)*(-4 + x)*(-3 + x) 5*(1 + x)*(-4 + x)*(-3 + x)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 2
(-4 + x) *(-3 + x)
$$\frac{\frac{4 \left(\frac{10 \delta\left(x + 1\right)}{\left|{x + 1}\right|^{\frac{3}{5}}} - \frac{3 \operatorname{sign}^{2}{\left(x + 1 \right)}}{\left|{x + 1}\right|^{\frac{8}{5}}} - \frac{10 \operatorname{sign}{\left(x + 1 \right)}}{\left(x + 1\right) \left|{x + 1}\right|^{\frac{3}{5}}} + \frac{25 \left|{x + 1}\right|^{\frac{2}{5}}}{\left(x + 1\right)^{2}}\right)}{125 \left(x + 1\right)} - \frac{\left(6 \left(5 x - 17\right) \left(\frac{1}{\left(x - 3\right)^{2}} + \frac{2}{\left(x - 4\right) \left(x - 3\right)} + \frac{2}{\left(x - 4\right)^{2}}\right) + \frac{2 \left(5 x - 17\right) \left(\frac{2}{x - 3} + \frac{3}{x - 4}\right)}{x - 3} + \frac{10 \left(5 x - 17\right)}{\left(x - 3\right)^{2}} + \frac{3 \left(5 x - 17\right) \left(\frac{2}{x - 3} + \frac{3}{x - 4}\right)}{x - 4} + \frac{24 \left(5 x - 17\right)}{\left(x - 4\right) \left(x - 3\right)} - \frac{2 \left(\frac{2}{x - 3} + \frac{3}{x - 4}\right) \left(\left(x - 4\right)^{2} + 6 \left(x - 4\right) \left(x - 3\right) + 3 \left(x - 3\right)^{2}\right)}{\left(x - 4\right) \left(x - 3\right)} - \frac{12 \left(\left(x - 4\right)^{2} + 6 \left(x - 4\right) \left(x - 3\right) + 3 \left(x - 3\right)^{2}\right)}{\left(x - 4\right) \left(x - 3\right)^{2}} + \frac{21 \left(5 x - 17\right)}{\left(x - 4\right)^{2}} - \frac{18 \left(\left(x - 4\right)^{2} + 6 \left(x - 4\right) \left(x - 3\right) + 3 \left(x - 3\right)^{2}\right)}{\left(x - 4\right)^{2} \left(x - 3\right)} + \frac{6 \left(3 \left(x - 4\right)^{2} + 6 \left(x - 4\right) \left(x - 3\right) + \left(x - 3\right)^{2}\right)}{\left(x - 4\right)^{2} \left(x - 3\right)}\right) \left|{x + 1}\right|^{\frac{2}{5}}}{\left(x - 4\right) \left(x - 3\right)} - \frac{6 \left(5 x - 17\right) \left(\frac{2 \operatorname{sign}{\left(x + 1 \right)}}{\left|{x + 1}\right|^{\frac{3}{5}}} - \frac{5 \left|{x + 1}\right|^{\frac{2}{5}}}{x + 1}\right)}{25 \left(x - 4\right) \left(x - 3\right) \left(x + 1\right)} + \frac{6 \left(\left(5 x - 17\right) \left(\frac{2}{x - 3} + \frac{3}{x - 4}\right) + \frac{2 \left(5 x - 17\right)}{x - 3} + \frac{3 \left(5 x - 17\right)}{x - 4} - \frac{2 \left(\left(x - 4\right)^{2} + 6 \left(x - 4\right) \left(x - 3\right) + 3 \left(x - 3\right)^{2}\right)}{\left(x - 4\right) \left(x - 3\right)}\right) \left|{x + 1}\right|^{\frac{2}{5}}}{5 \left(x - 4\right) \left(x - 3\right) \left(x + 1\right)}}{\left(x - 4\right)^{3} \left(x - 3\right)^{2}}$$