Question

obter a derivada da função y=(2x^2-3)^2 no ponto P(1,1)

Answer 1

lembrando que:
$\boxed{\boxed{\left(U^N\right)' = N*U^{N-1} * U'}}$

$y=(2x^2-3)^2\\\\y'=2(2x^2-3)^{2-1}*(2x^2-3)'\\\\y'=2(2x^2-3)*(2*2x^{2-1}-0)\\\\y'=2(2x^2-3)(4x)\\\\ y'=8x(2x^2-3)\\y'=16x^3-24x\\\\ \to\text{ para x=1}\\\\y'(1)=16*1^3 -24*1 =-8$