What is the derivative of lnx/x^2?

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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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` .

 

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