# What is the derivative of #sqrt(x ln(x^4))#?

##### 1 Answer

Mar 5, 2018

The trick to this problem is to break it down into a few steps.

#### Explanation:

- Take the derivative of the square root:

#sqrt(xln(x^4))=(xln(x^4))^(1/2)# , so the derivative is#1/2(xln(x^4))^(-1/2)=1/(2sqrt(xln(x^4)))# . - Take the derivative of the inside (product rule + chain rule):

So the derivative is,#(1)ln(x^4)+(x)(1/x^4)(4x^3)=ln(x^4)+4x^4/x^4=ln(x^4)+4# . - Therefore, our total derivative is:

#1/(2sqrt(xln(x^4)))(ln(x^4)+4)=(ln(x^4)+4)/(2sqrt(xln(x^4))# .