91Ó°ÊÓ

Find the derivative of each function by using the quotient rule. $$y=\frac{33 x}{4 x^{5}-3 x-4}$$

Find the derivative of each of the given functions. $$r=5\left(3 \theta^{6}-4\right)^{2 / 3}$$

Graph the function and determine the values of \(x\) for which the functions are continuous. Explain. $$f(x)=\left\\{\begin{array}{ll}\frac{x^{3}-x^{2}}{x-1} & \text { for } x \neq 1 \\\1 & \text { for } x=1\end{array}\right.$$

Find \(d y / d x\) by differentiating implicitly. When applicable, express the result in terms of \(x\) and \(y\). $$(2 x+1)(1-3 y)+y^{2}=13$$

Find the derivative of each of the functions by using the definition. $$y=\frac{5 x}{x-1}$$

Evaluate the derivative of each of the given functions at the given point. Check your result using the derivative evaluation feature of a calculator. $$s=2 t^{3}-5 t^{2} \quad(-1,-7)$$

Find the second derivative of each of the given functions. $$y=3\left(2 x^{3}+3\right)^{4}$$

Graph the function and determine the values of \(x\) for which the functions are continuous. Explain. $$f(x)=\left\\{\begin{array}{ll}\frac{2 x^{2}-18}{x-3} & \text { for } x \neq 3 \\\12 & \text { for } x=3\end{array}\right.$$

Evaluate the derivative of each of the given functions at the given point. Check your result using the derivative evaluation feature of a calculator. $$y=2 x^{3}+9 x-7 \quad(-2,-41)$$

Find the second derivative of each of the given functions. $$f(x)=\frac{2 \pi^{2}}{6-x}$$