Question

H(t) = (t +1)2\3(2t2-1)3... derivar na regra da cadeia...

Answer 1

$h(t) = (t+1)^{ \frac{2}{3} }*(2t^2-1)^3$

regra do produto
$U = (t+1)^{ \frac{2}{3} }\\\\U'= \frac{2}{3}(t+1) ^{ \frac{2}{3}-1 }(t+1)' = \frac{2}{3}(t+1)^{- \frac{1}{3} } \\\\\\\\V=(2t^2-1)^3\\\\V'=3(2t^2-1)^{3-1}(2t^2-1)' =3(2t^2-1)^2(4t+0) = 12t(t^2-1)^2\\\\.$

temos
$h'(t)= \frac{2}{3}(t+1)^{- \frac{1}{3} } *(2t^2-1)^3+ (t+1)^{ \frac{2}{3} }*12t(t^2-1)^2$