If `y=(1)/(sqrtx)=(x)^(-1//2)`, then find `dy//dx`.

Options

A. `-(1)/(2x^(1//2))`
B. `(1)/(2x^(3//2))`
C. `-(1)/(2x^(3//2))`
D. None of the Above

Answer

C

Explanation

Differentiating both sides w.r.t. x, we get
`(dy)/(dx)=(d[(x)^(-1//2)])/(dx)=-1/2x^(-(1//2)-1)=-1/2x^(-3//2)=-(1)/(2x^(3//2))`