If y = (log x)ˣ + x^(log x), then at x = e, dy/dx is:

If y = (log x)ˣ + x^(log x), then at x = e, dy/dx is:

• A. 3
• B. 2e
• C. e
• D. 1 + 2e

Answer: A) 3

Explanation: From earlier calculation, u′ = (log x)ˣ [log(log x) + 1/log x], v′ = x^(log x) [2 log x / x]. At x=e, log x=1, u=1, u′ = 1[0+1]=1. v=e, v′ = e[2/e]=2. Total = 3.