Question231) $y=\left(2 x^{3}-x^{2}+6 x+1\right)^{3}$

Studdy Solution
Apply the chain rule to find the derivative of $y$:
$$\frac{dy}{dx} = \frac{d}{du}(u^3) \cdot \frac{du}{dx}$$ $$\frac{dy}{dx} = 3u^2 \cdot (6x^2 - 2x + 6)$$
Substitute back the expression for $u$:
$$\frac{dy}{dx} = 3(2x^3 - x^2 + 6x + 1)^2 \cdot (6x^2 - 2x + 6)$$
The derivative of $y$ with respect to $x$ is:
$$\boxed{3(2x^3 - x^2 + 6x + 1)^2 (6x^2 - 2x + 6)}$$