Question

ALGUEM ME AJUDA POR FAVOR!!!!!

DERIVADA

f(x) = (x² − 2x + 5)(x³ + 2)

Answer 1

Vamos usar a regra do produto

$\text{f(x) ' }=[\ (\text x^2-2\text x+5)(\text x^3+2) \ ]' \\\\ \text {f(x) '} = (\text x^2-2\text x+5)'.(\text x^3+2)+(\text x^2-2\text x+5)(\text x^3+2)' \\\\ \text {f(x) '} = (2\text x-2).(\text x^3+2) + (\text x^2-2\text x+5)(3\text x^2) }$

Agora é só arrumar a expressão :

$\text{f(x) '} = 2\text x^4+4\text x-2\text x^3-4 + 3\text x^4 - 6\text x^3+15\text x^2 \\\\\\ \huge\boxed{\text {f(x) '} = 5\text x^4 -8\text x^3+15\text x^2+4 \text x-4 }\checkmark$