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- Derivada de una función implícitamente dada
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- Análisis de la función gráfica
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- Derivada de:
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Derivada de 9/2x
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Derivada de 8*y^3-64
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Derivada de (7x+5)'
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Derivada de (-9)/x^7-15*x^4+28/x^3+35*x^4-7
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Expresiones idénticas
- (x(x- cuatro))/((x+ dos)(x- cuatro)^ dos)^(dos / tres)
- (x(x menos 4)) dividir por ((x más 2)(x menos 4) al cuadrado ) en el grado (2 dividir por 3)
- (x(x menos cuatro)) dividir por ((x más dos)(x menos cuatro) en el grado dos) en el grado (dos dividir por tres)
- (x(x-4))/((x+2)(x-4)2)(2/3)
- xx-4/x+2x-422/3
- (x(x-4))/((x+2)(x-4)²)^(2/3)
- (x(x-4))/((x+2)(x-4) en el grado 2) en el grado (2/3)
- xx-4/x+2x-4^2^2/3
- (x(x-4)) dividir por ((x+2)(x-4)^2)^(2 dividir por 3)
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Expresiones semejantes
- (x(x-4))/((x+2)(x+4)^2)^(2/3)
- (x(x+4))/((x+2)(x-4)^2)^(2/3)
- (x(x-4))/((x-2)(x-4)^2)^(2/3)
Derivada de (x(x-4))/((x+2)(x-4)^2)^(2/3)
Solución
Ha introducido
[src]
x*(x - 4)
---------------------
2/3
/ 2\
\(x + 2)*(x - 4) /
$$\frac{x \left(x - 4\right)}{\left(\left(x - 4\right)^{2} \left(x + 2\right)\right)^{\frac{2}{3}}}$$
(x*(x - 4))/((x + 2)*(x - 4)^2)^(2/3)
Primera derivada
[src]
/ 2 \
|2*(x - 4) 2*(-8 + 2*x)*(x + 2)|
x*|---------- + --------------------|
1 \ 3 3 /
---------------------*(-4 + 2*x) - -------------------------------------
2/3 4/3 5/3 4/3
(x + 2) *|x - 4| (x - 4)*(x + 2) *|x - 4|
$$- \frac{x \left(\frac{2 \left(x - 4\right)^{2}}{3} + \frac{2 \left(x + 2\right) \left(2 x - 8\right)}{3}\right)}{\left(x - 4\right) \left(x + 2\right)^{\frac{5}{3}} \left|{x - 4}\right|^{\frac{4}{3}}} + \frac{1}{\left(x + 2\right)^{\frac{2}{3}} \left|{x - 4}\right|^{\frac{4}{3}}} \left(2 x - 4\right)$$
Segunda derivada
[src]
/ / 6*(-2 + x) / 1 2*sign(-4 + x)\ 3*x 6*x \ \
| x*|- ---------- + 2*x*|----- + --------------| + ----- + ------| |
| \ -4 + x \2 + x |-4 + x| / 2 + x -4 + x/ 4*x*(-2 + x) |
2*|1 + ---------------------------------------------------------------- - ----------------|
\ 3*(2 + x) (-4 + x)*(2 + x)/
-------------------------------------------------------------------------------------------
2/3 4/3
(2 + x) *|-4 + x|
$$\frac{2 \left(\frac{x \left(2 x \left(\frac{2 \operatorname{sign}{\left(x - 4 \right)}}{\left|{x - 4}\right|} + \frac{1}{x + 2}\right) + \frac{3 x}{x + 2} + \frac{6 x}{x - 4} - \frac{6 \left(x - 2\right)}{x - 4}\right)}{3 \left(x + 2\right)} - \frac{4 x \left(x - 2\right)}{\left(x - 4\right) \left(x + 2\right)} + 1\right)}{\left(x + 2\right)^{\frac{2}{3}} \left|{x - 4}\right|^{\frac{4}{3}}}$$
Tercera derivada
[src]
/ / / 1 2*sign(-4 + x)\ / 1 2*sign(-4 + x)\ / 1 2*sign(-4 + x)\ \ \
| | / 2 \ 6*(-2 + x)*|----- + --------------| 3*x*|----- + --------------| 6*x*|----- + --------------| | |
| | 9 | 5 12*DiracDelta(-4 + x) 14*sign (-4 + x) 8*sign(-4 + x) | 36*(-2 + x) 12*x 27*x 24*(-2 + x) \2 + x |-4 + x| / \2 + x |-4 + x| / \2 + x |-4 + x| / 24*x 12*(-2 + x)*sign(-4 + x) 6*x*sign(-4 + x) 12*x*sign(-4 + x)| |
| x*|------ + x*|-------- - --------------------- + ---------------- + ----------------| - ----------- + -------- + --------- - ---------------- - ----------------------------------- + ---------------------------- + ---------------------------- + ---------------- - ------------------------ + ---------------- + -----------------| / 6*(-2 + x) / 1 2*sign(-4 + x)\ 3*x 6*x \|
| |-4 + x | 2 |-4 + x| 2 (2 + x)*|-4 + x|| 2 2 2 (-4 + x)*(2 + x) -4 + x 2 + x -4 + x (-4 + x)*(2 + x) (-4 + x)*|-4 + x| (2 + x)*|-4 + x| (-4 + x)*|-4 + x|| (-2 + x)*|- ---------- + 2*x*|----- + --------------| + ----- + ------||
| 3*x \ \(2 + x) (-4 + x) / (-4 + x) (2 + x) (-4 + x) / \ -4 + x \2 + x |-4 + x| / 2 + x -4 + x/|
4*|- ------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------|
\ -4 + x 9 -4 + x /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5/3 4/3
(2 + x) *|-4 + x|
$$\frac{4 \left(- \frac{x \left(x \left(- \frac{12 \delta\left(x - 4\right)}{\left|{x - 4}\right|} + \frac{8 \operatorname{sign}{\left(x - 4 \right)}}{\left(x + 2\right) \left|{x - 4}\right|} + \frac{5}{\left(x + 2\right)^{2}} + \frac{14 \operatorname{sign}^{2}{\left(x - 4 \right)}}{\left(x - 4\right)^{2}}\right) + \frac{3 x \left(\frac{2 \operatorname{sign}{\left(x - 4 \right)}}{\left|{x - 4}\right|} + \frac{1}{x + 2}\right)}{x + 2} + \frac{6 x \operatorname{sign}{\left(x - 4 \right)}}{\left(x + 2\right) \left|{x - 4}\right|} + \frac{12 x}{\left(x + 2\right)^{2}} + \frac{6 x \left(\frac{2 \operatorname{sign}{\left(x - 4 \right)}}{\left|{x - 4}\right|} + \frac{1}{x + 2}\right)}{x - 4} + \frac{12 x \operatorname{sign}{\left(x - 4 \right)}}{\left(x - 4\right) \left|{x - 4}\right|} + \frac{24 x}{\left(x - 4\right) \left(x + 2\right)} + \frac{27 x}{\left(x - 4\right)^{2}} - \frac{6 \left(x - 2\right) \left(\frac{2 \operatorname{sign}{\left(x - 4 \right)}}{\left|{x - 4}\right|} + \frac{1}{x + 2}\right)}{x - 4} - \frac{12 \left(x - 2\right) \operatorname{sign}{\left(x - 4 \right)}}{\left(x - 4\right) \left|{x - 4}\right|} - \frac{24 \left(x - 2\right)}{\left(x - 4\right) \left(x + 2\right)} + \frac{9}{x - 4} - \frac{36 \left(x - 2\right)}{\left(x - 4\right)^{2}}\right)}{9} - \frac{3 x}{x - 4} + \frac{\left(x - 2\right) \left(2 x \left(\frac{2 \operatorname{sign}{\left(x - 4 \right)}}{\left|{x - 4}\right|} + \frac{1}{x + 2}\right) + \frac{3 x}{x + 2} + \frac{6 x}{x - 4} - \frac{6 \left(x - 2\right)}{x - 4}\right)}{x - 4}\right)}{\left(x + 2\right)^{\frac{5}{3}} \left|{x - 4}\right|^{\frac{4}{3}}}$$