Posted by Ali on .
If √x+√y=10 and y(16)=36, find y'(16) by implicit differentiation.
If somebody could please help me by explaining how to solve this problem ! Thank you (:

Calculus [Implicit Differentiation] 
Steve,
just take d/dx of each term in the equation. (f+g)' = f' + g', so you can treat each term on its ow.
Recall that dx/dx = 1, so
√x+√y=10
1/(2√x) dx/dx + 1/(2√y) dy/dx = 0
1/(2√x) + 1/(2√y) y' = 0
at x=16, y=36, so
1/(2*4) + 1/(2*6) y' = 0
y' = (1/8) * 12 = 3/2