Question

differentiate rootx-1/rootx​

Answer 1

Differentiation of (√x -1/√x) :-

Take LCM:-

» d/dx (x-1/√x)

Apply Quotient Rule:

d/dx (u/v) = (v.du/dx - u.dv/dx)/v²

» (√x(1) - (x-1)(1/2√x))/√x²

» (√x - (x-1/2√x))/x

» (2x - x + 1)/2x√x

» (x+1)/2x√x