Question

Find the derivative of the function. y = tan2(8θ)

Answer 1

16tan(8θ)sec²(8θ)

Explanation:

Given the question :

Find the derivative of the function. y = tan2(8θ)

y = tan²(8θ)

USing chain rule :

dy/dx = (du/dx) × (dv/du) × (dy/dv)

Let u = 8θ ; du/dθ = 8

v = tan u ; dv/du = sec²u

y = v² ; dy/dv = 2v

Hence,

(dy/dθ) × dv/du × dy/dv

8 * sec²u * 2v

Where v = tan u ; u = 8θ

8 * sec²8θ * 2tan8θ

16tan(8θ)sec²(8θ)