Question

resolva a derivada

f(x) = x/(x²-1)^4

Answer 1

$\mathsf{\dfrac{d}{dx}(\dfrac{u}{v})=\dfrac{\dfrac{du}{dx}.v-u.\dfrac{dv}{dx}}{{v}^{2}}}$

$\mathsf{f(x)=\dfrac{x}{{({x}^{2}-1)}^{4}}}\\\mathsf{f'(x)=\dfrac{1.{({x}^{2}-1)}^{4}-x.4{(x^{2}-1)}^{3}.2x}{{({[x^{2}-1]}^{4})}^{2}}}$

$\mathsf{f'(x)=\dfrac{{(x^{2}-1)}^{4}-8x^{2}{(x^{2}-1)}^{3}}{{(x^{2}-1)}^{8}}}$