Question

How do you differentiate `f(x)=(x+1)/sqrtx` using the quotient rule?

Answer 1

`f'(x)=(x-1)/(xsqrtx)`

Explanation:

Let `f(x)=(x+1)/sqrtx`. To find `f'`, we will use the quotient rule

`d/dxu/v=(vu'-uv')/v^2`

So

`f'(x)=d/dx(x+1)/sqrtx=(sqrtxd/dx(x+1)-(x+1)d/dxsqrtx)/(sqrtx)^2=(sqrtx-(x+1)/(2sqrtx))/x=(2x-x-1)/(2xsqrtx)=(x-1)/(2xsqrtx)`