Answer
$$ - \frac{1}{5}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}f\left( x \right) = - 5x + 4;\,\,\,\,\,\left( { - 1,1} \right) \cr
& {\text{Calculate }}f'\left( 1 \right) \cr
& f'\left( x \right) = - 5 \cr
& f'\left( 1 \right) = - 5 \cr
& {\text{Find the derivative of the inverse function}}{\text{, using the THEOREM 3}}{\text{.23}} \cr
& \left( {{f^{ - 1}}} \right)'\left( {{y_0}} \right) = \frac{1}{{f'\left( {{x_0}} \right)}},\,\,\,\,{\text{Where }}{y_0} = f\left( {{x_0}} \right) \cr
& {\text{Then}}{\text{,}} \cr
& \left( {{f^{ - 1}}} \right)'\left( 1 \right) = \frac{1}{{f'\left( { - 1} \right)}} \cr
& \left( {{f^{ - 1}}} \right)'\left( 1 \right) = \frac{1}{{ - 5}} \cr
& \left( {{f^{ - 1}}} \right)'\left( 1 \right) = - \frac{1}{5} \cr} $$
