Differentiate, with respect to x, e^3x + ln 2x,
e^3x differentiates to 3e^3x as you multiply the function e^3x by the derivative of the inside function 3x. 3x differentiates to 3, so the answer is 3 multiplied by e^3x. The derivative of a natural log function is the multiplication of the derivative of the inside function which 1/x. In this case, 2x differentiates to 2, so the answer is 2 multiplied by 1/x = 2/x.
So the answer is 3e^3x + 2/x.
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