Find `(dy)/(dx)` when :
`y=6x^(100)-x^(55)+x`

Answer

To find \(\frac{dy}{dx}\) for the function \(y = 6x^{100} - x^{55} + x\), we will use the power rule of differentiation. The power rule states that if \(y = x^n\), then \(\frac{dy}{dx} = n \cdot x^{n-1}\).

### Step-by-step solution:

1. **Identify the function**:
\[ y = 6x^{100} - x^{55} + x \]

2. **Differentiate each term separately**:
- For the first term \(6x^{100}\):
\[ \frac{d}{dx}(6x^{100}) = 6 \cdot 100 \cdot x^{100-1} = 600x^{99} \]
- For the second term \(-x^{55}\):
\[ \frac{d}{dx}(-x^{55}) = -55 \cdot x^{55-1} = -55x^{54} \]
- For the third term \(x\):
\[ \frac{d}{dx}(x) = 1 \]

3. **Combine the derivatives**:
Now, we will combine the results from each term:
\[ \frac{dy}{dx} = 600x^{99} - 55x^{54} + 1 \]

### Final Answer:
\[ \frac{dy}{dx} = 600x^{99} - 55x^{54} + 1 \]