91Ó°ÊÓ

In Exercises \(1-28\) , find \(d y / d x\) . Remember that you can use NDER to support your computations. $$y=x^{2} e^{x}-x e^{x}$$

In Exercises \(1-10,\) find \(d y / d x\) . Use your grapher to support your analysis if you are unsure of your answer. $$y=\frac{x}{1+\cos x}$$

In Exercises \(1-8,\) use the given substitution and the Chain Rule to find \(d y / d x\) $$y=\sec (\tan x), u=\tan x$$

In Exercises \(9-12,\) a particle moves along the \(x\) -axis so that its position at any time \(t \geq 0\) is given by \(x(t) .\) Find the velocity at the indicated value of \(t .\) $$x(t)=\sin ^{-1}\left(\frac{t}{4}\right), \quad t=3$$

In Exercises \(7-12,\) find the horizontal tangents of the curve. $$y=x^{4}-4 x^{2}+1$$

In Exercises \(9-12,\) find \(d y / d x\) and find the slope of the curve at the indicated point. $$x^{2}+y^{2}=13, \quad(-2,3)$$

In Exercises \(1-10,\) find \(d y / d x\) . Use your grapher to support your analysis if you are unsure of your answer. $$y=\frac{\cot x}{1+\cot x}$$

In Exercises \(1-28\) , find \(d y / d x\) . Remember that you can use NDER to support your computations. $$y=e^{\sqrt{x}}$$

In Exercises \(7-12,\) find the horizontal tangents of the curve. $$y=4 x^{3}-6 x^{2}-1$$

In Exercises \(9-12,\) a particle moves along the \(x\) -axis so that its position at any time \(t \geq 0\) is given by \(x(t) .\) Find the velocity at the indicated value of \(t .\) $$x(t)=\sin ^{-1}\left(\frac{\sqrt{t}}{4}\right), \quad t=4$$