Question

Qual o resultado usando a regra do quociente para f'(x) de f(x) = (2x+5) / (4x) ?

Answer 1

$\displaystyle \sf \underline{Regra\ do \ Quociente}}: \\\\ \left[\frac{f}{g} \right]' = \frac{f'\cdot g-f\cdot g'}{g^2} \\\\\\ temos : \\\\ f(x) = \frac{2x+5}{4x} \\\\ derivando : \\\\ f'(x) = \frac{(2x+5)'\cdot 4x-(2x+5)\cdot (4x)'}{(4x)^2} \\\\\\ f'(x) = \frac{(2)\cdot 4x-(2x+5)\cdot 4}{16x^2} \\\\\\ f'(x) = \frac{8x-8x-20}{16x^2} \\\\\\ f'(x) = \frac{-20}{16x^2} \\\\\\ \boxed{\sf f'(x) = \frac{-5}{4x^2}}\checkmark$