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

Answer

To determine whether the statement \( \frac{dy}{dx} = e^x \) is true or false given that \( y = e^x \), we can follow these steps:

### Step 1: Identify the function
We are given the function:
\[ y = e^x \]

### Step 2: Differentiate the function
To find \( \frac{dy}{dx} \), we need to differentiate \( y \) with respect to \( x \):
\[ \frac{dy}{dx} = \frac{d}{dx}(e^x) \]

### Step 3: Apply the differentiation rule
The derivative of \( e^x \) with respect to \( x \) is:
\[ \frac{d}{dx}(e^x) = e^x \]

### Step 4: Write the result
Thus, we have:
\[ \frac{dy}{dx} = e^x \]

### Conclusion
Since we found that \( \frac{dy}{dx} = e^x \), the statement is **True**.

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