Question

help me in this question of limit...​

Answer 1

By the definition of a derivative,

$f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Here, $f(x) = x^{\frac{1}{5}}$

Therefore,

$f'(x) = \frac{1}{5x^{\frac{4}{5}}}$

Which is the answer to the limit.

i.e $\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$ = $\frac{1}{5x^{\frac{4}{5}}}$

You could also directly apply L'hopital rule but it's extra work imo.