What is the derivative of lnx/x^2?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Let `f(x)= lnx/x^2`

`` We will use the quotient rule to find the derivative.

We know that if `f(x)= u/v, ==gt f'(x)= (u'v-uv')/v^2`

`` ==> `f(x)= lnx/x^2`

`` ==> Let `u = lnx ==gt u' = 1/x`

`` ==> Let `v = x^2 ==gt v' = 2x`

`` ==> `f'(x)= (1/x x^2 - lnx*2x)/(x^2)^2`

`` ==> `f'(x)= ( x - 2xlnx)/x^4 = (x(1-2lnx))/x^4 = (1-2lnx)/x^3`

`` ==> The derivative of `lnx/x^2`  is `f'(x)= (1-2lnx)/x^3` .


See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team