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

Engineering

Mathematics

Derivative of Inverse Function

Question

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

1 + {g(x)}⁵

1 + x⁵

5x⁴

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

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g'(y) = $\frac{1}{f' (x)}$ = 1 + x⁵

g'(x) = 1 + (g(x))⁵