Question

obtenha a função derivada de f(x)=x^2/tgx

Answer 1

$\boxed{y = \frac{u}{v} \Rightarrow y' = \frac{u' v - u v'}{v^{2}}}$

u = x² ⇒ u' = 2x
v = tg(x) ⇒ v' = sec²(x)

$y = \frac{x^{2}}{tg(x)} \Rightarrow y' = \frac{2x \cdot tg(x) - x^{2} sec^{2}(x)}{[tg(x)]^{2}} = \boxed{\frac{x[2 tg(x) - x sec^2(x)]}{tg^{2}(x)}}$