Question

Задана функция F(x) = 31-2x /x-4 найдите f´(1)

Answer 1

$F(x) = \frac{3^{1-2x}}{x^{-4}}$
$F'(x) = \frac{(3^{1-2x})'*(x^{-4}) -(3^{1-2x})*(x^{-4})'}{(x^{-4})^2} = \frac{(3^{1-2x})*ln3*(-2)*x^{-4} +4x^{-3}(3^{1-2x})}{x^{-8}} =$
$= \frac{(3^{1-2x})(-2x^4*ln3+4x^3)}{x^{-8}}$
$f'(1)= \frac{(3^{1-2*1})(-2*1^4*ln3+4*1^3)}{1^{-8}} =3^{-1}*(-2ln3+4) = \frac{-2ln3+4}{3}$