- #1
cal.queen92
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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!