Find `dy/dx if y=5x^2-3bx-a`

Answer

To find \(\frac{dy}{dx}\) for the function \(y = 5x^2 - 3bx - a\), we will differentiate each term of the function with respect to \(x\).

### Step-by-Step Solution:

1. **Identify the function**:
\[ y = 5x^2 - 3bx - a \]

2. **Differentiate each term**:
- The first term is \(5x^2\):
- Using the power rule \(\frac{d}{dx}(x^n) = nx^{n-1}\), we differentiate \(5x^2\):
\[ \frac{d}{dx}(5x^2) = 5 \cdot 2x^{2-1} = 10x \]

- The second term is \(-3bx\):
- Here, \(-3b\) is a constant multiplier. The derivative of \(x\) is \(1\):
\[ \frac{d}{dx}(-3bx) = -3b \cdot 1 = -3b \]

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

3. **Combine the derivatives**:
Now, we can combine the derivatives of each term:
\[ \frac{dy}{dx} = 10x - 3b - 0 \]

4. **Final result**:
Thus, the derivative of \(y\) with respect to \(x\) is:
\[ \frac{dy}{dx} = 10x - 3b \]