Question

What will be the value of dy/dx if x = asec^2θ and y = atan^3θ at θ = π/4?

(a) 1/2

(b) 3/4

(c) 3/2

(d) 1/4

The question was asked in a job interview.

This question is from First Order Derivative in section Limits and Derivatives of Mathematics – Class 11

Answer 1

Correct answer is (c) 3/2

Explanation: Since, x = asec^2θ,

Therefore, dx/dθ = a*d/dx(sec^2θ)

= 2asecθ*secθ tanθ

Again, dy/dθ = a*d/dx(tan^3θ)

= a * 3 tan^2θ * d/dθ(tanθ)

= 3a tan^2θ sec^2θ

 Therefore, dy/dx = (dy/dθ)/(dx/dθ)

= 3a tan^2θ sec^2θ/2asecθ*secθ tanθ

Thus, at θ = π/4 we have,

dy/dx = 3/2(tan π/4)

= 3/2