91Ó°ÊÓ

Find \(f^{\prime}(x)\). $$f(x)=\frac{\cot x}{1+\csc x}$$

$$\text { Find } f^{\prime}(x)$$. $$f(x)=\frac{x^{2}}{3 x-4}$$

Find \(f^{\prime}(x)\) $$f(x)=\sqrt{4+\sqrt{3 x}}$$

A function \(y=f(x)\) and values of \(x_{0}\) and \(x_{1}\) are given. (a) Find the average rate of change of \(y\) with respect to \(x\) over the interval \(\left[x_{0}, x_{1}\right]\). (b) Find the instantaneous rate of change of \(y\) with respect to \(x\) at the specified value of \(x_{0}\). (c) Find the instantaneous rate of change of \(y\) with respect to \(x\) at an arbitrary value of \(x_{0}\). (d) The average rate of change in part (a) is the slope of a certain secant line, and the instantaneous rate of change in part (b) is the slope of a certain tangent line. Sketch the graph of \(y=f(x)\) together with those two lines. $$y=1 / x ; x_{0}=2, x_{1}=3$$

$$\text { Find } f^{\prime}(x)$$ $$f(x)=x^{e}+\frac{1}{x^{\sqrt{10}}}$$

A function \(y=f(x)\) and values of \(x_{0}\) and \(x_{1}\) are given. (a) Find the average rate of change of \(y\) with respect to \(x\) over the interval \(\left[x_{0}, x_{1}\right]\). (b) Find the instantaneous rate of change of \(y\) with respect to \(x\) at the specified value of \(x_{0}\). (c) Find the instantaneous rate of change of \(y\) with respect to \(x\) at an arbitrary value of \(x_{0}\). (d) The average rate of change in part (a) is the slope of a certain secant line, and the instantaneous rate of change in part (b) is the slope of a certain tangent line. Sketch the graph of \(y=f(x)\) together with those two lines. $$y=1 / x^{2} ; x_{0}=1, x_{1}=2$$

$$\text { Find } f^{\prime}(x)$$ $$f(x)=\sqrt[3]{\frac{8}{x}}$$

Find \(f^{\prime}(x)\). $$f(x)=\frac{\sec x}{1+\tan x}$$

Find \(f^{\prime}(x)\) $$f(x)=\sqrt[3]{12+\sqrt{x}}$$

$$\text { Find } f^{\prime}(x)$$. $$f(x)=\frac{2 x^{2}+5}{3 x-4}$$