Question

Y=1/(x^5 -x+1)^9 derivada?

Answer 1

y =1. (x^5 - x + 1)^ -9
y' = 1.(-9)(x^5 - x +1)^-10 . (5x^4 - 1) + 0.(x^5 - x + 1)
y'= -9(x^5 - x + 1)^-10.(5x^4 - 1)
OU
5x^4 - 1 / [-9(x^5 - x + 1)^10]

Answer 2

$\boxed{\boxed{\dfrac{d(u^{n})}{dx}=n\cdot u^{n-1}\cdot\dfrac{du}{dx}}}$
______________________

$y=\dfrac{1}{(x^{5}-x+1)^{9}}~~~\therefore~~~y=(x^{5}-x+1)^{-9}$

$\boxed{u=x^{5}-x+1}~~~\boxed{n=-9}$

Derivando:

$y'=\dfrac{d(x^{5}-x+1)^{-9}}{dx}\\\\\\y'=-9\cdot(x^{5}-x+1)^{-9-1}\cdot\dfrac{d(x^{5}-x+1)}{dx}\\\\\\y'=-9\cdot(x^{5}-x+1)^{-10}\cdot(5x^{4}-1)\\\\\\y'=\dfrac{-9\cdot(5x^{4}-1)}{(x^{5}^-x+1)^{10}}\\\\\\\boxed{\boxed{y'=\dfrac{9-45x^{4}}{(x^{5}-x+1)^{10}}}}$