How do you find the derivative of $root6(x^5)$ ?

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Answer 1 · 2018-04-12T05:14:34

$=5/(6root(6)x)$

$f(x)=root(6)(x^5)=x^(5/6)$
$d/dx f(x)=5/6x^(5/6-1)$
$=5/6x^(-1/6)$
$=5/(6root(6)x)$

Answer 2 · 2018-04-12T05:16:11

Derivative of $root(6)x^5$ is $5/(6root(6)x)$

The derivative of $x^n$ is $nx^(n-1)$

As we can write $root(6)x^5=x^(5/6)$

$d/(dx)root(6)x^5=5/6x^(5/6-1)$

= $5/6x^(-1/6)$

= $5/6*1/root(6)x$

= $5/(6root(6)x)$

How do you find the derivative of root6(x^5)root6(x^5)?