Find the derivatives of the following :
`a/x^(4)-b/x^(2)+cosx`

Answer

To find the derivative of the function \( y = \frac{a}{x^4} - \frac{b}{x^2} + \cos x \), we will differentiate each term separately.

### Step-by-Step Solution:

1. **Identify the function**:
\[ y = \frac{a}{x^4} - \frac{b}{x^2} + \cos x \]

2. **Rewrite the function using negative exponents**:
\[ y = ax^{-4} - bx^{-2} + \cos x \]

3. **Differentiate each term**:
- For the first term \( ax^{-4} \):
\[ \frac{dy}{dx} = a \cdot (-4) x^{-5} = -\frac{4a}{x^5} \]
- For the second term \( -bx^{-2} \):
\[ \frac{dy}{dx} = -b \cdot (-2) x^{-3} = \frac{2b}{x^3} \]
- For the third term \( \cos x \):
\[ \frac{dy}{dx} = -\sin x \]

4. **Combine the derivatives**:
\[ \frac{dy}{dx} = -\frac{4a}{x^5} + \frac{2b}{x^3} - \sin x \]

5. **Final result**:
\[ \frac{dy}{dx} = -\frac{4a}{x^5} + \frac{2b}{x^3} - \sin x \]