`sqrt(5x -4)`

Answer

` 5/(2(2-3x)^(3/2))`

Explanation

`y=sqrt(5x-4)Rightarrow (y + deltay)=sqrt(5(x+deltax)-4)`
`Rightarrow (deltay)/(dx) = (sqrt(5(x+deltax)-4)- sqrt(5x-4))/(deltax)`
`:. (dy)/(dx) = lim_(deltax to 0) (deltay)/(deltax)`
`= lim_(deltaxto0) ({sqrt(5(x+deltax)-4)-sqrt(5x-4)})/(deltax) xx ({sqrt(5(x+deltax)-4)+sqrt(5x-4)})/({sqrt(5(x+deltax)-4)+sqrt(5x-4)})`
`= lim_(deltax to0) 5/({sqrt5(x+deltax)-4+sqrt(5x-4)})=5/(2sqrt(5x-4))`
Hence ` d/(dx) (sqrt(5x-4)) = 5/(2sqrt(5x -4))`