Find `(dy)/(dx)` for the following :
`y=ax^(2)+bx+c`

Answer

To find \(\frac{dy}{dx}\) for the function \(y = ax^2 + bx + c\), we will differentiate each term of the function with respect to \(x\).

### Step-by-Step Solution:

1. **Identify the function**:
The function given is:
\[ y = ax^2 + bx + c \]

2. **Differentiate each term**:
We will apply the power rule of differentiation, which states that if \(y = x^n\), then \(\frac{dy}{dx} = nx^{n-1}\).

- For the first term \(ax^2\):
- Here, \(a\) is a constant and we differentiate \(x^2\):
\[ \frac{d}{dx}(ax^2) = a \cdot 2x^{2-1} = 2ax \]

- For the second term \(bx\):
- Here, \(b\) is a constant and we differentiate \(x\):
\[ \frac{d}{dx}(bx) = b \cdot 1x^{1-1} = b \]

- For the third term \(c\):
- Since \(c\) is a constant, its derivative is:
\[ \frac{d}{dx}(c) = 0 \]

3. **Combine the derivatives**:
Now, we combine the results from the differentiation of each term:
\[ \frac{dy}{dx} = 2ax + b + 0 \]
Therefore, we simplify this to:
\[ \frac{dy}{dx} = 2ax + b \]

### Final Result:
The derivative of the function \(y = ax^2 + bx + c\) with respect to \(x\) is:
\[ \frac{dy}{dx} = 2ax + b \]