Derivative of f(x)?

Question

f(x)=x*sqaure root(2x-3)
find Derivative.


THanks!

Answer 1

f ( x ) = (x) (2 x - 3)^(1/2)

f `( x ) is:-
(1)(2 x - 3)^(1/2) + (1/2)(2 x - 3)^(-1/2) (2)( x )
(2 x - 3)^(1/2) + (x) (2 x - 3)^(-1/2)
(2 x - 3)^(-1/2) [ (2 x - 3) + x ]
(3 x - 3) / (2 x - 3)^(1/2)
(3) (x - 1) / (2 x - 3)^(1/2)

Answer 2

f(x)=x*2(sqrt2x-3)

let u=x*2 v=sqrt(2x-3)
du/dx=2x using Chain Rule or direct derivative...yields

dv/dx=1/sqrt(2x-3)

Using Product Rule,

df(x)/dx = udv/dx + vdu/dx
=x*2(1/sqrt(2x-3)+sqrt(2x-3)(2x)
=x*2/sqrt(2x-3)+sqrt(2x-3)(2x)