# How do you differentiate #g(x) = e^(2x)ln3x# using the product rule?

I found:

According to the Product Rule, if you have:

In your situation, after deriving each function, you must additionally apply the Chain Rule (highlighted in red) to obtain:

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To differentiate ( g(x) = e^{2x} \ln(3x) ) using the product rule, follow these steps:

- Identify the two functions being multiplied: ( f(x) = e^{2x} ) and ( h(x) = \ln(3x) ).
- Apply the product rule: ( g'(x) = f'(x)h(x) + f(x)h'(x) ).
- Find the derivatives of each function: ( f'(x) = 2e^{2x} ) and ( h'(x) = \frac{1}{x} ).
- Substitute these derivatives into the product rule formula: ( g'(x) = 2e^{2x} \ln(3x) + e^{2x} \cdot \frac{1}{x} ).
- Simplify the expression if necessary.

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