How do you find the derivative of #ln (x^8)/ x^2#?

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Answer 1 · 2016-05-07T22:33:45

In this case, you would use quotient rule.

Before we get started, check this out. Here is the definition for quotient rule.

#f(x)=g(x)/(h(x))#

#f'(x)=(h(x)g'(x) - h'(x)g(x))/(h(x))^2#

So know what we know the definition, let's apply it. We know that #g(x)=ln(x^8)# and #h(x)=x^2#. So now, it's just plug n' solve.

#f'(x)=(x^2((8x^7)/(x^8))-2x(ln(x^8)))/(x^4)#

And I would personally be satisfied with the below answer.

#f'(x)=(8x-2xln(x^8))/(x^4)#