Question

olá colegas me ajude neste exercicio por favor.
utilizando a regra de derivação , calcule F(x)= -sen²x /x

Answer 1

$\displaystyle f(x)=\frac{-\sin^2(x)}{x}\\\\ \frac{d}{dx}\frac{-\sin^2(x)}{x}=\frac{d}{dx}\frac{u}{v}=\frac{u'\cdot v+v'\cdot u}{v^2}\\\\ \frac{d}{dx}-\sin^2(x)=-2\sin(x)\cdot\cos(x)=u'\\\\\frac{d}{dx}x=1=v'\\\\\frac{df}{dx}=\frac{u'\cdot v +v'\cdot u}{v^2}=\boxed{\frac{-2x\sin(x)\cos(x)+\sin^2(x)}{x^2}}$