If y ` = e^(log x ) , then ( dy)/(dx) `

Options

A. ` e^(log x ) `
B. ` (1)/(x) `
C. ` 0`
D. `1`

Answer

To solve the problem, we need to find the derivative of the function \( y = e^{\log x} \).

### Step-by-Step Solution:

1. **Identify the function**:
Given \( y = e^{\log x} \).

2. **Use the property of logarithms**:
We can simplify \( e^{\log x} \) using the property of logarithms which states that \( e^{\log_a b} = b \) when the base of the logarithm is \( e \). Here, since the base of the logarithm is \( e \), we can simplify:
\[ y = x \]

3. **Differentiate the function**:
Now we need to differentiate \( y \) with respect to \( x \):
\[ \frac{dy}{dx} = \frac{d}{dx}(x) \]

4. **Calculate the derivative**:
The derivative of \( x \) with respect to \( x \) is:
\[ \frac{dy}{dx} = 1 \]

### Final Answer:
Thus, the derivative \( \frac{dy}{dx} \) is:
\[ \frac{dy}{dx} = 1 \]