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

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Answer 1 · 2018-03-05T00:24:38

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

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

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