Find `dy/dx if y= e^x-2x`

Answer

To find \(\frac{dy}{dx}\) for the function \(y = e^x - 2x\), we will differentiate the function with respect to \(x\).

### Step-by-Step Solution:

1. **Identify the function**:
\[ y = e^x - 2x \]

2. **Differentiate \(y\) with respect to \(x\)**:
We will apply the rules of differentiation. The derivative of \(e^x\) is \(e^x\), and the derivative of \(2x\) is \(2\).

\[ \frac{dy}{dx} = \frac{d}{dx}(e^x) - \frac{d}{dx}(2x) \]

3. **Calculate the derivatives**:
- The derivative of \(e^x\) is \(e^x\).
- The derivative of \(2x\) is \(2\).

Thus, we have:
\[ \frac{dy}{dx} = e^x - 2 \]

4. **Final result**:
Therefore, the derivative \(\frac{dy}{dx}\) is:
\[ \frac{dy}{dx} = e^x - 2 \]