Question

Derivada de
$f(x)=cotg3x^2$

Answer 1

$\\ y = cotg3x^2 \\ \\ y' = (cotg3x^2)'*(3x^2)' \\ \\ y' = -cossec^2(3x^2)*2*3x^2^-^1 \\ \\ y' = -cossec^2(3x^2)*6x$

Answer 2

$\sf \displaystyle \:f\left(x\right)=cotg~3x^2\\\\\\\frac{d}{df\left(x\right)}\left(cf\left(x\right)\tan \left(3\right)x^2\right)\\\\\\{Tratar}\:c,\:x\:{como\:constante}\\\\\\{Retire\:a\:constante}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\\\=ctan \left(3\right)x^2\frac{d}{df\left(x\right)}\left(f\left(x\right)\right)\\\\\\{Aplique\:a\:regra\:da\:derivação}:\quad \frac{d}{df\left(x\right)}\left(f\left(x\right)\right)=1\\\\\\=ctan \left(3\right)x^2\cdot \:1$

$\to \boxed{\sf =tan \left(3\right)cx^2}$