F'(x) of (x)(sq rt of 2x-3)?

Question

please help and show me how it's done!

Answer 1

If you want to take the derivative of a function that is the product of two other functions, like h(x)=f(x)g(x)... you take the derivative of the first times the second, plus the derivative of the second times the first... that is, h'(x)=f'(x)g(x)+g'(x)f(x).

So here it's:

(1)(sqrt(2x-3))+(x)(1/2)((2x-3)^(-1/2)...

= sqrt(2x-3) - x/(sqrt(2x-3))