Find `dy/dx if y=x-tanx`

Answer

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

### Step-by-step Solution:

1. **Write down the function**:
We start with the function given in the problem:
\[ y = x - \tan x \]

2. **Differentiate both sides with respect to \(x\)**:
We apply the differentiation operator to both sides:
\[ \frac{dy}{dx} = \frac{d}{dx}(x) - \frac{d}{dx}(\tan x) \]

3. **Differentiate \(x\)**:
The derivative of \(x\) with respect to \(x\) is:
\[ \frac{d}{dx}(x) = 1 \]

4. **Differentiate \(\tan x\)**:
The derivative of \(\tan x\) with respect to \(x\) is:
\[ \frac{d}{dx}(\tan x) = \sec^2 x \]

5. **Combine the results**:
Now, substituting the derivatives back into the equation, we get:
\[ \frac{dy}{dx} = 1 - \sec^2 x \]

### Final Result:
Thus, the derivative \(\frac{dy}{dx}\) is:
\[ \frac{dy}{dx} = 1 - \sec^2 x \]