Question

A2. Find y' and y" for y^2 = x^2
+ sinxy

Answer 1

y' = (2x + y cosxy)/(2y + x cosxy)

Explanation:

Using implicit differentiation:

y^2 = x^2 + sin xy

2y y' = 2x + cos xy * (xy' + y)

2y y' = 2x + xy' cos xy + y cos xy

2y y' - xy' cosxy = 2x + ycos xy

y' = (2x + y cosxy)/(2y - x cosxy)