Question

1. Suppose xy = 20, where x and y are functions of t. What
is the value of dx/dt when x = 4 and dy/dt = -2?
(A) - 1.6
(B) 20
(C) 1.6
(D) 2.5​

Answer 1

Answer:

(c) 1.6

Step-by-step explanation:

Given, xy = 20 and both x, y are functions of t.

So,

⇒ $\frac{d(xy)}{dt} = x\frac{dy}{dt} + y\frac{dx}{dt}$

now, when x = 4, y will be 5 as xy = 20.

by subtituting the values in above equation, we get;

⇒ $\frac{d(20)}{dt} = 4(-2) + 5\frac{dx}{dt}$

⇒ $0 = -8 + 5\frac{dx}{dt}$

⇒ $\frac{dx}{dt} = \frac{8}{5}$

⇒ $\frac{dx}{dt} = 1.6$