I am getting the 0, but its not right. What am I doing wrong??????
If and , find by implicit differentiation.
sqrt(x) +sqrt(y) = 7
Differentiate both sides with respect to x,
1/(2sqrt(x)) +[1/(2sqrt(y)](y') = 0
y' = -[1 / 2sqrt(x)] / [1 / 2sqrt(y)]
y' = -[1 /sqrt(x)] * [sqrt(y) / 1]
y' = -sqrt(y) / sqrt(x)
y' = -sqrt(y/x)
y(16) = 9
So, point (16,9)
y'(16) = -sqrt(9/16) = +,-3/4 ----------------answer.