Question Detail

MTH 102 Differentiation Objective Question

Question

Differentiate \( y = e^{x \ln x} \).
Options
A \( e^{x \ln x} (1 + \ln x) \)
Correct Answer
B \( e^{x \ln x} \)
C 1
D \( (1 + \ln x) \)
Correct Answer

Option A is the correct answer.

Detailed Explanation

Chain rule: ( e^{x \ln x} ) times derivative of exponent ( x \ln x ), which is ( 1 + \ln x ). Note: this is same as ( x^x ).

Hint

Identify the inner function in the exponent.

Question Info