Find the Derivative - d/dx 5^(3x)

Problem

d(5(3*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 d(au)/d(x)=au⋅ln(a)⋅d(u)/d(x) to the expression, where a=5 and u=3*x

3. Differentiate the exponent u=3*x with respect to x which gives (d(3)*x)/d(x)=3

4. Substitute the derivative of the exponent back into the formula to get 5(3*x)⋅ln(5)⋅3

5. Simplify the expression by rearranging the constants.

Final Answer

d(5(3*x))/d(x)=3⋅5(3*x)*ln(5)

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