Question

How do you differentiate `f(x)=[2(ln x)]/sqrtx`?

Answer 1

`f'(x)=(2-lnx)/x^(3/2)`

Explanation:

According to the Quotient Rule:

`f'(x)=(sqrtxd/dx[2lnx]-2lnxd/dx[sqrtx])/(sqrtx)^2`

`f'(x)=((2sqrtx)/x-lnx/sqrtx)/x`

`f'(x)=((2x-xlnx)/(xsqrtx))/x`

`f'(x)=((2-lnx)/sqrtx)/x`

`f'(x)=(2-lnx)/x^(3/2)`