Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. xy = 6
(a) Find dy/dt, given x = 4 and dx/dt = 11.
dy/dt =

(b) Find dx/dt, given x = 1 and dy/dt = –9.
dx/dt =

A)

B)

Step-by-step explanation:

x and y are differentiable functions of t, and we are given the equation:

First, let's differentiate both sides of the equation with respect to t. So:

By the Product Rule and rewriting:

Therefore:

A)

We want to find dy/dt when x = 4 and dx/dt = 11.

Using our original equation, find y when x = 4:

Therefore:

Solve for dy/dt:

B)

We want to find dx/dt when x = 1 and dy/dt = -9.

Again, using our original equation, find y when x = 1:

Therefore:

Solve for dx/dt:

it will cost dollar $540

the living room is 3 which means if we divide 325/3 then we get $108

therefore if 1part of the living room cost $108 and 3 costed $325

then total 5part of the room will cost 5*108 which gives $540