Question

Let x and y be differentiable functions of t and suppose that they are related by the equation xy-1=y^2. Find dx/dt when x=2 and d/y=1.

Need the solution and answer rn​

Answer 1

Answer:

Given u=f(x,y) is a a differentiable function of x and y, where x,y are differentiable functions of t.

We have to find

dt

du

Since x,y are differentiable functions of t

Let x=g(t),y=h(t)

Thus by chain rule we get

dt

du

=

∂x

∂f

⋅

dt

dx

+

∂y

∂f

⋅

dt

dy

Answer 2

Let x and y be differentiable functions of t and suppose that they are related by the equation xy-1=y^2. Find dx/dt when x=2 and d/y=1.