Question

Derivada de (4x^2-3)^2(x+5)^3

Answer 1

$\displaystyle \sf \left [(4x^2-3)^2\cdot(x+5)^3 \right]' \\\\ \text{Aplicando a regra do produto}} : \\\\ \left[(4x^2-3)^2\right]'\cdot (x+5)^3+(4x^2-3)^2\cdot \left[(x+5)^3 \right]' \\\\ \underline{\text{Ao derivar aplique a regra da cadeia}}: \\\\ 2\cdot (4x^2-3)\cdot (4x^2-3)'\cdot (x+5)^3+(4x^2-3)^2\cdot 3\cdot(x+5)^2\cdot (x+5)' \\\\ 2(4x^2-3)\cdot (8x)\cdot (x+5)^3+3(4x^2-3)^2\cdot (x+5)^2\cdot (1) \\\\ \boxed{\ \sf16x\cdot(4x^2-3)\cdot (x+5)^3+3\cdot(4x^3-3)^2\cdot (x+5)^2 \ }\checkmark$