Find the derivative of the following function. \[ f(x)=\frac{x^{3}-9 x^{2}+x}{x-1} \]

Find the indefinite integral. \( \int \frac{1}{2+5 x^{6}}\left(30 x^{5}\right) d x \) \( \int \frac{1}{2+5 x^{6}}\left(30 x^{5}\right) \cdot d x=\square \)

Find \( C_{x y}(x, y) \) if \( C(x, y)=8 x^{2}+3 x y-9 y^{2}+3 x-3 y-3 \) \( C_{x y}(x, y)=\square \)

Find \( f^{\prime}(x) \). \( f(x)=\left(3 x^{5}+4\right)^{3} \) \( f^{\prime}(x)=\square \)

Use L'Hôpital's rule to find the following limit and check the answer using an algebraic simplification. \( \lim _{x \rightarrow 8} \frac{x^{2}-x-56}{x-8} \) \( \lim _{x \rightarrow 8} \frac{x^{2}-x-56}{x-8}=\square \) (Simplify your answer.)

Find the indicated derivative. \[ y^{\prime} \text { for } y=\left(3 x^{3}+5 x^{2}\right)(4 x-3) \] \( y^{\prime}=\square \)