Question

derivada de (x^2+1)^3 (2x^2+5x-3)^-2

Answer 1

$f(x) = (x^2+1)^3\cdot(2x^2+5x-3)^{-2}\\\\Regra\ do\ Produto\\\\f'(x)=g'(x).h(x)+g(x).h'(x)\\\\g(x)=(x^2+1)^3\ e\ h(x)=(2x^2+5x-3)^{-2}\\\\Regra\ da\ Cadeia\\\\g'(x)=6x\cdot(x^2+1)^2\\\\h'(x)= \dfrac{-2\cdot(4x+5)}{(2x^2+5x-3)^{3}}$

$f'(x)=6x\cdot(x^2+1)^2\cdot(2x^2+5x-3)^{-2}+(x^2+1)^3\cdot{ \dfrac{-2\cdot(4x+5)}{(2x^2+5x-3)^{3}} }\\\\\\f'(x)= \dfrac{(6x^3+6x)^2}{(2x^2+5x-3)^2}+ \dfrac{(x^2+1)^3\cdot(-8x-10)}{(2x^2+5x-3)^3}$