Differentiate, e^3x + ln 2x

To differentiate e^3x + ln(2x) with respect to x, we can use the rules of differentiation. 

The derivative of e^u with respect to x is given by d/dx(e^u) = e^u * du/dx, where u is a function of x.

Similarly, the derivative of ln(u) with respect to x is given by d/dx(ln(u)) = (1/u) * du/dx.

Let’s find the derivative of each term separately:

d/dx(e^3x) = e^3x * d/dx(3x) = 3e^3x

d/dx(ln(2x)) = (1/(2x)) * d/dx(2x) = (1/(2x)) * 2 = 1/x

Therefore, the derivative of e^3x + ln(2x) with respect to x is:

3e^3x + 1/x.

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