Find the Derivative - d/dX y=3^(2X)

Problem

d()/d(x)*3^(2*x)

Solution

1. Identify the rule for differentiating an exponential function of the form a^u which is d(a^u)/d(x)=a^u*ln(a)d(u)/d(x)

2. Apply the chain rule by setting u=2*x which means d(u)/d(x)=2

3. Substitute the values into the derivative formula: d(3^(2*x))/d(x)=3^(2*x)*ln(3)⋅2

4. Simplify the expression by rearranging the constants.

Final Answer

d(3^(2*x))/d(x)=2⋅3^(2*x)*ln(3)

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