If f(x)= |cosxl, then `f'((3pi)/4)` equal to -

Options

A. `(-1)/(sqrt(2))`
B. `(1)/(sqrt(2))`
C. 1
D. none of these

Explanation

To solve the problem, we need to find the derivative of the function \( f(x) = |\cos x| \) at the point \( x = \frac{3\pi}{4} \).

### Step-by-step Solution:

1. **Identify the function**:
\[ f(x) = |\cos x| \]

2. **Determine the value of \( \cos \left( \frac{3\pi}{4} \right) \)**:
\[ \cos \left( \frac{3\pi}{4} \right) = -\frac{1}{\sqrt{2}} \quad (\text{since } \frac{3\pi}{4} \text{ is in the second quadrant}) \]

3. **Remove the modulus**:
Since \( \cos \left( \frac{3\pi}{4} \right) \) is negative, we can express \( f(x) \) without the modulus:
\[ f(x) = -\cos x \]

4. **Differentiate the function**:
\[ f'(x) = \frac{d}{dx}(-\cos x) = \sin x \]

5. **Evaluate the derivative at \( x = \frac{3\pi}{4} \)**:
\[ f'\left( \frac{3\pi}{4} \right) = \sin\left( \frac{3\pi}{4} \right) \]

6. **Calculate \( \sin \left( \frac{3\pi}{4} \right) \)**:
\[ \sin \left( \frac{3\pi}{4} \right) = \frac{1}{\sqrt{2}} \quad (\text{since } \frac{3\pi}{4} \text{ is in the second quadrant}) \]

7. **Final result**:
\[ f'\left( \frac{3\pi}{4} \right) = \frac{1}{\sqrt{2}} \]

### Conclusion:
The value of \( f'\left( \frac{3\pi}{4} \right) \) is \( \frac{1}{\sqrt{2}} \).