Solution: What is the first derivative of the expression (xy)^x = e?

What is the first derivative of the expression (xy)^x = e? How to find the derivative using the product rule involving exponential function and natural logarithm?

What is the first derivative of the expression (xy)^x = e?

Problem Statement: ME Board April 1997

What is the first derivative of the expression (xy)x = e?
  • A. 0
  • B. x/y
  • C. –y [(1 + ln xy) / x)]
  • D. –y [(1 – ln xy) / x2)]

Problem Answer:

The derivative is equal to –y[(1 + ln xy)/x)]

Solution:

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