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

1 Answer
Nov 24, 2015

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)