-1 ------- 3*x - 8 (x*x + 2*x)
(x*x + 2*x)^(-1/(3*x - 8))
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Perola derivada
Simplificamos:
Respuesta:
-1 ------- 3*x - 8 /3*log(x*x + 2*x) 2 + 2*x \ (x*x + 2*x) *|---------------- - ---------------------| | 2 (3*x - 8)*(x*x + 2*x)| \ (3*x - 8) /
/ 2 \ -1 |/ 3*log(x*(2 + x)) 2*(1 + x)\ | -------- ||- ---------------- + ---------| 2 | -8 + 3*x |\ -8 + 3*x x*(2 + x)/ 18*log(x*(2 + x)) 2 4*(1 + x) 12*(1 + x) | (x*(2 + x)) *|--------------------------------- - ----------------- - --------- + ----------- + --------------------| | -8 + 3*x 2 x*(2 + x) 2 2 x*(-8 + 3*x)*(2 + x)| \ (-8 + 3*x) x *(2 + x) / ---------------------------------------------------------------------------------------------------------------------------- -8 + 3*x
/ / 2 \ \ | 3 / 3*log(x*(2 + x)) 2*(1 + x)\ | 1 9*log(x*(2 + x)) 2*(1 + x) 6*(1 + x) | | -1 |/ 3*log(x*(2 + x)) 2*(1 + x)\ 6*|- ---------------- + ---------|*|- --------- - ---------------- + ----------- + --------------------| | -------- ||- ---------------- + ---------| \ -8 + 3*x x*(2 + x)/ | x*(2 + x) 2 2 2 x*(-8 + 3*x)*(2 + x)| 3 2 | -8 + 3*x |\ -8 + 3*x x*(2 + x)/ 162*log(x*(2 + x)) 18 12*(1 + x) \ (-8 + 3*x) x *(2 + x) / 16*(1 + x) 36*(1 + x) 108*(1 + x) | -(x*(2 + x)) *|--------------------------------- - ------------------ - -------------------- - ----------- + -------------------------------------------------------------------------------------------------------- + ----------- + ---------------------- + ---------------------| | 2 3 x*(-8 + 3*x)*(2 + x) 2 2 -8 + 3*x 3 3 2 2 2 | \ (-8 + 3*x) (-8 + 3*x) x *(2 + x) x *(2 + x) x *(-8 + 3*x)*(2 + x) x*(-8 + 3*x) *(2 + x)/ --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -8 + 3*x