Find `dy/dx if x^(3)-lambdax^(2)+11x-6=y`

Answer

To find \(\frac{dy}{dx}\) for the equation \(y = x^3 - \lambda x^2 + 11x - 6\), we will differentiate \(y\) with respect to \(x\).

### Step-by-step Solution:

1. **Start with the given equation:**
\[ y = x^3 - \lambda x^2 + 11x - 6 \]

2. **Differentiate each term with respect to \(x\):**
- The derivative of \(x^3\) is:
\[ \frac{d}{dx}(x^3) = 3x^2 \]
- The derivative of \(-\lambda x^2\) is:
\[ \frac{d}{dx}(-\lambda x^2) = -\lambda \cdot 2x = -2\lambda x \]
- The derivative of \(11x\) is:
\[ \frac{d}{dx}(11x) = 11 \]
- The derivative of the constant \(-6\) is:
\[ \frac{d}{dx}(-6) = 0 \]

3. **Combine the derivatives:**
Putting it all together, we have:
\[ \frac{dy}{dx} = 3x^2 - 2\lambda x + 11 \]

### Final Result:
Thus, the derivative \(\frac{dy}{dx}\) is:
\[ \frac{dy}{dx} = 3x^2 - 2\lambda x + 11 \]