maths help pls! quadratic equation....?

Question

the curve C has the equation y = 9root(x) + 27/x + 5
(a) find dy/dx
(b) find the value of dy/dx when x = 9
been puzzling over this for ages and just can't get it!

Answer 1

(a) y' = 9*(1/2)x^(-1/2) - 27/x^2. You use the power rule, which states that d/dx[x^n] = nx^(n-1). In the first term, you have n=1/2, and in the second term, you have n=-1.
(b) plug in x=9, and you get (9/2)9^(-1/2) - 27/9^2
= (9/2)(1/3) - 27/81 = 3/2 - 1/3 = 7/6.