Find the Derivative - d/dx a^x

Problem

d(a^x)/d(x)

Solution

1. Use the exponential identity to rewrite the expression in terms of the natural base e Since a^x=e^ln(a^x) we use the property of logarithms to write a^x=e^(x*ln(a))

2. Apply the chain rule for the derivative of e^u where u=x*ln(a)

3. Differentiate the exponent with respect to x Since ln(a) is a constant, the derivative of x*ln(a) is simply ln(a)

4. Multiply the results to find the final derivative.

Final Answer

d(a^x)/d(x)=a^x*ln(a)

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