Question

How do you differentiate `f(x)=(x^(1/2))(lnx)`?

Answer 1

`1/(2sqrtx) lnx+ 1/sqrtx`

Explanation:

This needs to be differentiated using the product rule:

`d/dxf(x)g(x)=g(x)f'(x)+f(x)g'(x)`

`d/dx x^(1/2)= 1/2x^(-1/2)= 1/(2sqrtx)`

`d/dxlnx= 1/x`

`d/dxf(x)=1/(2sqrtx)lnx+sqrtx/x=1/(2sqrtx)+1/sqrtx`