Question

Find the derivative of \( a^x \): \[ \frac{d}{dx} \left( a^x \right) \]

• A. \( a^x \log a \)
• B. \( a^x \log x \)
• C. \( a^x \)
• D. \( \log a \)

Hint:

Remember that the derivative of \( a^x \) is not the same as \( e^x \). Use \( \frac{d}{dx} \left( a^x \right) = a^x \log a \), where \( \log a \) is the natural logarithm of \( a \).

Answer 1

The Correct Option is A

To differentiate an exponential function with base \( a \) (where \( a>0 \) and \( a \neq 1 \)), we use the formula: \[ \frac{d}{dx} \left( a^x \right) = a^x \log a \] Hence, the derivative of \( a^x \) is: \[ \boxed{a^x \log a} \]