Question

If Δ(x) = |(sin2x, e^xsinx + x cosx, sinx + x²cosx), (cosx + sinx, e^x + x, 1 + x²), (e^xcosx, e^2x, e^x)|, then

(A) Δ'(0) = 0

(B) Δ'(π/2) = 0

(C) Δ'(π/4) = 0

(D) All the above

Answer 1

Answer is (D) All the above

We can write Δ(x) as product of two determinants as follows:

which is independent of (x)⇒ Δ′ (x) = 0 ∀ x.