Question

find the derivative of the function x^​(3/​7)​

Answer 1

$\large \sf \: x ^ { \frac { 3 } { 7 } }$

The derivative of ax^n is nax^n - 1. So..

$\sf \: x ^{ \frac{3}{7} } \\ = \sf\frac{3}{7}x^{\frac{3}{7}-1}$

Subtract 1 from 3/7 (in the exponents).

$\sf\frac{3}{7}x^{\frac{3}{7}-1} \\ = \sf \: \frac{3}{7}x^{-\frac{4}{7}} \\ \sf \: = \boxed{ \sf\frac{3}{7x^{\frac{4}{7}}}}$

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