Question

If y = (3x – 4)/(x+2) then what s the value of dy/dx?

(a) dy/dx

(b) y

(c) 1/ (dy/dx)

(d) A constant

The question was posed to me during an online exam.

Enquiry is from First Order Derivative in division Limits and Derivatives of Mathematics – Class 11

Answer 1

Correct option is (c) 1/ (dy/dx)

To explain: It is given that y = (3x – 4)/(x + 2) ……….(1)

Now differentiating both the sides, we get that,

dy/dx = (x + 2)*3 – (3x – 4)/(x + 2)^2

= 10/(x + 2)^2

Again from (1) we get,

xy + 2y = 3x – 4

or, x = – 2(y + 2)

Thus dx/dy = -2* ((y – 3) – (y + 2))/ (y – 3)^2

Or, y – 3 = (3x – 4)/(x + 2) – 3

= -10/(x + 2)

Thus, dx/dy = 10/(-10/(x + 2))^2

= (x + 2)2/10, where,x ≠ 0 i.e. dx/dy ≠ 0

Therefore, dy/dx*dx/dy = 10/(x + 2)2 * -10/(x + 2)

= 1

=> dy/dx = 1/(dy/dx)