suppose that x x t and y y t and

Question

Suppose that x = x (t ) and y = y (t ) and differentiate the following equation with respect to t.

Solution                                        x³ y⁶ + e^{1- x} - cos (5 y ) = y ²

Thus, just differentiate as normal & add on proper derivative at each step. Note that the first term will be a product rule as both x and y is functions of t.

                             3x² x′y⁶ + 6x³ y⁵ y′ - x′e^{1- x} + 5 y′ sin (5 y) = 2 yy′

There actually isn't all that much to this problem.  As there are two derivatives in the problem we won't be bothering to solve out for one of them. 

At this point there doesn't appear be any real purpose for doing this kind of problem,