Question

What is the derivate for `2013root2013x` ?

Answer 1

`1/root2013(x^2012)`

Explanation:

Rewrite the radical using `rootnx=x^(1//n)`:

`2013root2013x=2013x^(1//2013)`

Now use the power rule: `d/dxx^n=nx^(n-1)`. Note that `1/2013-1=(-2012)/2013`

`d/dx2013x^(1//2013)=2013(1/2013)x^((-2012)/2013)`

`=1/x^(2012/2013)=1/root2013(x^2012)`