Question

O valor da derivada da função f(x)=x-3/2x+4 no ponto que x=2:

Answer 1

Resposta:

Explicação passo-a-passo:

$f(x)=\dfrac{x-3}{2x+4}$

Devemos usar a regra da divisão para efetuar essa derivada

$f(x)=\dfrac{u}{v}\\\\f'(x)=\dfrac{u'.v-u.v'}{v^{2}}\\\\Aplicando\\\\\\f'(x)=\dfrac{1.(2x+4)-(x-3).2}{(2x+4)^{2}}\\\\\\f'(x)=\dfrac{2x+4-2x+6}{(2x+4)^{2}}\\\\\\f'(x)=\dfrac{10}{4x^{2}+16x+16}\\\\\\f'(x)=\dfrac{2.5}{2.(2x^{2}+8x+8)}\\\\\\f'(x)=\dfrac{5}{2x^{2}+8x+8}$

Para x=2 teremos

$f'(2)=\dfrac{5}{2.2^{2}+8.2+8}\\\\\\f'(2)=\dfrac{5}{8+16+8}\\\\\\f'(2)=\dfrac{5}{32}\\\\\\\boxed{f'(2)=0,15625}$