Question

qual a derivada da função f(t)= sen²(3t²-1)

Answer 1

$f(t)= \sin^2(3t^2-1)$

$u=3t^2-1$

$f(t)=\sin^2u$

$v=\sin u$

$f(t)=v^2$

$u'=6t$

$v'=u'\cdot\cos u$
$v'=6t\cos u$

$f'(t)=v'\cdot(2v)$
$f'(t)=(6t\cos u)(2v)$
$f'(t)=12tv\cos u$
$f'(t)=12t\sin u\cdot\cos u$
$f'(t)=12t\sin (3t^2-1)\cdot\cos (3t^2-1)$