Find the Derivative - d/dx 3^(2x)

Problem

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

Solution

1. Identify the rule for differentiating an exponential function of the form au where a is a constant and u is a function of x

2. Apply the formula for the derivative of au which is d(au)/d(x)=au⋅ln(a)⋅d(u)/d(x)

3. Substitute the values a=3 and u=2*x into the formula.

4. Differentiate the exponent u=2*x with respect to x which gives (d(2)*x)/d(x)=2

5. Combine the terms to find the final derivative.

Final Answer

d(3(2*x))/d(x)=2⋅3(2*x)*ln(3)

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