Find `(dy)/(dx)` when :
`y=x^(8)/8-x^(6)/6+x^(4)/4-2`

Answer

To find \(\frac{dy}{dx}\) for the function

\[ y = \frac{x^8}{8} - \frac{x^6}{6} + \frac{x^4}{4} - 2, \]

we will differentiate each term of the function with respect to \(x\).

### Step 1: Differentiate each term

1. **Differentiate \(\frac{x^8}{8}\)**:
- Using the power rule, \(\frac{d}{dx}(x^n) = nx^{n-1}\):
\[ \frac{d}{dx}\left(\frac{x^8}{8}\right) = \frac{1}{8} \cdot 8x^{8-1} = x^7. \]

2. **Differentiate \(-\frac{x^6}{6}\)**:
- Again using the power rule:
\[ \frac{d}{dx}\left(-\frac{x^6}{6}\right) = -\frac{1}{6} \cdot 6x^{6-1} = -x^5. \]

3. **Differentiate \(\frac{x^4}{4}\)**:
- Using the power rule:
\[ \frac{d}{dx}\left(\frac{x^4}{4}\right) = \frac{1}{4} \cdot 4x^{4-1} = x^3. \]

4. **Differentiate \(-2\)**:
- The derivative of a constant is 0:
\[ \frac{d}{dx}(-2) = 0. \]

### Step 2: Combine the derivatives

Now, we combine the results from the differentiation:

\[ \frac{dy}{dx} = x^7 - x^5 + x^3 + 0. \]

Thus, we can simplify this to:

\[ \frac{dy}{dx} = x^7 - x^5 + x^3. \]

### Final Answer

The derivative \(\frac{dy}{dx}\) is:

\[ \frac{dy}{dx} = x^7 - x^5 + x^3. \]

---