Finally, substitute for .
Try these solved problems without looking at the answers. Then check your work.
PROBLEM 1. Find if x^2 + y^2 =6xy.
Answer: Differentiate with respect to x.
2 x + 2 y = 6x + 6 yGroup all of the terms on the left and the other terms on the right.
2 y − 6x = 6 y − 2xNow factor out .
(2 y − 6x) = 6 y − 2xTherefore, the first derivative is the following:
PROBLEM 2. Find if x − cos y = xy.
Answer: Differentiate with respect to x.
1 + sin y = x + y