First slide

Derivatives

Question

$If g is the inverse of a function f and f^{'} (x) = \frac{1}{1 + x^{5}} then g^{'} (x) is equal to$

Moderate

A

$\frac{1}{1 + {\{g (x)\}}^{5}}$
B

$1 + {\{g (x)\}}^{5}$
C

$1 + x^{5}$
D

$5 x^{4}$

Solution

g is the inverse of
$f \Rightarrow f o g (x) = x \Rightarrow (f o g)' (x) = 1 \Rightarrow f' [g (x)] g' (x) = 1 \Rightarrow g' (x) = \frac{1}{f' [g (x)]} = 1 + {[g (x)]}^{5}$

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