Question

Suppose xy = 15, where x and y are functions of t. What is the value of dx/dt when x = 3 and dy/dt = −2?

Options:
A) 15
B) 2.5
C) −1.2
D) 1.2

Answer 1

The value of dx/dt when x = 3 and dy/dt = −2 is 1.2.

We can solve this problem using implicit differentiation:

Start with the given equation: xy = 15

Differentiate both sides of the equation with respect to t:

d/dt (xy) = d/dt (15)

x(dy/dt) + y(dx/dt) = 0

Substitute the given values:

3(-2) + y(dx/dt) = 0

-6 + y(dx/dt) = 0

Solve for dx/dt:

y(dx/dt) = 6

dx/dt = 6 / y

Plug in the value of x:

dx/dt = 6 / (15/3)

dx/dt = 6 / 5

Therefore, the value of dx/dt when x = 3 and dy/dt = −2 is 1.2.