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

Options

A. 0
B. x
C. e
D. 1

Answer

To find the derivative of the function \( y = e^{\log_e x} \), we can follow these steps:

### Step 1: Simplify the function
We start with the function:
\[ y = e^{\log_e x} \]
Using the property of logarithms that states \( e^{\log_e a} = a \), we can simplify this expression:
\[ y = x \]

### Step 2: Differentiate the function
Now that we have simplified \( y \) to \( x \), we can differentiate it with respect to \( x \):
\[ \frac{dy}{dx} = \frac{d}{dx}(x) \]
The derivative of \( x \) with respect to \( x \) is:
\[ \frac{dy}{dx} = 1 \]

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

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