`(d(a^(x)))/(dx)=`

Options

A. `a^(x)`
B. `log(a^(x))`
C. `a^(x)loga`
D. `xa^(x-1)`

Answer

To differentiate the function \( a^x \) with respect to \( x \), we can use the following steps:

### Step-by-Step Solution:

1. **Identify the function**: We need to differentiate the function \( f(x) = a^x \), where \( a \) is a constant.

2. **Use the differentiation rule for exponential functions**: The differentiation of \( a^x \) can be expressed using the natural logarithm. The formula for the derivative of \( a^x \) is:
\[ \frac{d}{dx}(a^x) = a^x \ln(a) \]

3. **Apply the formula**: Now, we apply the formula to our function:
\[ \frac{d}{dx}(a^x) = a^x \ln(a) \]

4. **Final result**: Therefore, the derivative of \( a^x \) with respect to \( x \) is:
\[ \frac{d(a^x)}{dx} = a^x \ln(a) \]