If y = (sin x)ᵗᵃⁿ ˣ, then dy/dx at x = π/4 is:
If y = (sin x)ᵗᵃⁿ ˣ, then dy/dx at x = π/4 is:
- A. (√2/2)(1 − log 2)
- B. (1/√2) log 2
- C. 1/2
- D. 0
Answer: A) (√2/2)(1 − log 2)
Explanation: ln y = tan x · log sin x, so y′/y = sec²x · log sin x + 1. At x = π/4: sec²x = 2, sin x = 1/√2, giving 2(−½ log 2) + 1 = 1 − log 2 and y = √2/2. So y′ = (√2/2)(1 − log 2).
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