Find the derivative of the function \( f(x)=-\frac{x^{3}}{x-1} \)

Evaluate the function. If the value is not a rational number, rouna (a) \( \operatorname{csch}^{-1}(3) \) (b) \( \operatorname{coth}^{-1}(6) \)

Find the average rate of change of \( f(x)=-2 x^{2}-x \) from \( x=2 \) to \( x=6 \), Simplify your answer as much as possible.

Consider the following. \[ y=\sinh \left(4-x^{2}\right),(2,0) \] Find \( y^{\prime} \) Find the slope of the line tangent to the graph of \( y \) at the given point. Find an equation of the tangent line to the graph of the function at the given point. .

Find an equation of the tangent line to the graph of the function at the point \( (1,1) \). \[ y=x^{\cosh (x)} \] \( y=\square \)

Find the indefinite integral. (Remember the constant of integration.)