Find the Derivative - d/dx a^x

Problem

d(ax)/d(x)

Solution

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

2. Apply the chain rule for the derivative of eu 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(ax)/d(x)=ax*ln(a)

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