91Ó°ÊÓ

find the second derivative of the function. $$ f(x)=\frac{x+1}{x-1} $$

Find the value of the derivative of the function at the given point. State which differentiation rule you used to find the derivative. $$\begin{array}{ll}{\text { Function }} & {\text { Point }} \\\\{g(x)=\frac{2 x+1}{x-5}} & {(6,13)} \end{array}$$

Find the derivative of the function. $$ f(t)=-3 t^{2}+2 t-4 $$

Volume All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each edge is (a) 1 centimeter and (b) 10 centimeters?

Find \(d y / d x\) by implicit differentiation and evaluate the derivative at the given point. Equation \(\quad\) Point \(x^{2}+y^{2}=16\) \(\quad\) \((0,4)\)

Find \(d y / d x\) by implicit differentiation and evaluate the derivative at the given point. Equation \(\quad\) Point \(x^{2}-y^{2}=25\) \(\quad\) \((5,0)\)

Find the derivative of the function. $$ y=x^{3}-9 x^{2}+2 $$

Find \(d y / d u, d u / d x,\) and \(d y / d x.\) $$ y=u^{-1}, u=x^{3}+2 x^{2} $$

Surface Area All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the surface area changing when each edge is (a) 1 centimeter and (b) 10 centimeters?

Find the value of the derivative of the function at the given point. State which differentiation rule you used to find the derivative. $$\begin{array}{ll}{\text { Function }} & {\text { Point }} \\\\{f(x)=\frac{ x+1}{x-1}} & {(2,3)} \end{array}$$