Question

Dada a função determine o valor de f ' (1). Escolha uma : a. 2 b. 3 c. 7 d. 22 e. 11

Answer 1

Regra da cadeia:

$f(x)=v(u(x))\to f'(x)=u'(x)\cdot v'(u)$

Logo:

$u(x)=8x^3-x^2+4\to u'(x)=24x^2-2x\\\\v(u)=\ln(u)\to v'(u)=\dfrac1u\\\\\\f'(x)=(24x^2-2x)\cdot\dfrac1u=\dfrac{24x^2-2x}{8x^3-x^2+4}\\\\\\f'(1)=\dfrac{24x^2-2x}{8x^3-x^2+4}=\dfrac{24(1)^2-2(1)}{8(1)^3-(1)^2+4}=\dfrac{22}{11}=2$