Find, the derivative of the following w.r.t. x :
`x^(-3/4)`

Answer

To find the derivative of the function \( y = x^{-\frac{3}{4}} \) with respect to \( x \), we can use the power rule of differentiation. The power rule states that if \( y = x^n \), then the derivative \( \frac{dy}{dx} = n \cdot x^{n-1} \).

### Step-by-step Solution:

1. **Identify the function**:
\[ y = x^{-\frac{3}{4}} \]

2. **Apply the power rule**:
According to the power rule, we differentiate \( y \) with respect to \( x \):
\[ \frac{dy}{dx} = -\frac{3}{4} \cdot x^{-\frac{3}{4} - 1} \]

3. **Simplify the exponent**:
Calculate the new exponent:
\[ -\frac{3}{4} - 1 = -\frac{3}{4} - \frac{4}{4} = -\frac{7}{4} \]
Thus, we can rewrite the derivative:
\[ \frac{dy}{dx} = -\frac{3}{4} \cdot x^{-\frac{7}{4}} \]

4. **Final expression**:
Therefore, the derivative of \( y = x^{-\frac{3}{4}} \) with respect to \( x \) is:
\[ \frac{dy}{dx} = -\frac{3}{4} x^{-\frac{7}{4}} \]

### Final Answer:
\[ \frac{dy}{dx} = -\frac{3}{4} x^{-\frac{7}{4}} \]