Question

The derivative of f(tan x) w.r.t. g(sec x) at x = π/4 where f(1) = 2 and g(√2) =4, is

• A. (A) 12
• B. (B) √2
• C. (C) 1
• D. (D) 2

Answer 1

Answer: (A)

(A) 12

Answer 2

Explanation:
Let u=f(tan⁡x) and v=g(sec⁡x)∴dudx=f′(tan⁡x)⋅sec2⁡xand dvdx=g∗(sec⁡x)⋅sec⁡xtan⁡x∴dudv=du/dxdv/dx=f(tan⁡x)⋅sec2⁡x8′(sec⁡x)⋅sec⁡xtan⁡x=f′(tan⁡x)sec⁡xg′(sec⁡x)tan⁡xAt x=π4,dudv=f′(1)secπg′(2)tanπ=2×24×1=12