- #1

cal.queen92

- 43

- 0

## Homework Statement

If (sqrt x) + (sqrt y) = 11 and f(9)=64 ---> find f '(9) by implicit differentiation

## The Attempt at a Solution

I keep getting lost in my work here...

first, taking derivative of both sides:

d/dx ((sqrt x) + (sqrt y)) = d/dx (11)

obtaining: (1/2)(x)^(-1/2) + (1/2)(y)^(-1/2) * dy/dx = 0

Now, I want to keep y positive so:

(1/2)(y)^(-1/2) * dy/dx = -(1/2)(x)^(-1/2)

So if I solve for dy/dx:

dy/dx = (-1/(sqrt x)) / (1/(sqrt y)) which means: dy/dx = (-1/(sqrt x) * ((sqrt y)/1)

giving: dy/dx = -(sqrt y)/ (sqrt x) as the derivative.

However, I don't know how to use the other information provided! I am very stuck... If anyone has any ideas, thanks!