91Ó°ÊÓ

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

In Exercises \(1-8,\) find the derivative of \(y\) with respect to the appropriate variable. $$y=\cos ^{-1}\left(x^{2}\right)$$

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

In Exercises \(1-8,\) find \(d y / d x\). $$x^{2} y+x y^{2}=6$$

In Exercises \(1-6,\) find \(d y / d x\). $$y=-x^{2}+3$$

In Exercises \(1-8,\) use the given substitution and the Chain Rule to find \(d y / d x\) . $$y=\sin (3 x+1), u=3 x+1$$

In Exercises 1-4, use the definition \(f^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}\) to find the derivative of the given function at the indicated point. \(f(x)=1 / x, a=2\)

(a) Write the volume \(V\) of a cube as a function of the side length \(s\) . (b) Find the (instantaneous) rate of change of the volume V with respect to a side s. (c) Evaluate the rate of change of \(V\) at \(s=1\) and \(s=5\) (d) If \(s\) is measured in inches and \(V\) is measured in cubic inches, what units would be appropriate for \(d V / d s ?\)

In Exercises 1-4, use the definition \(f^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}\) to find the derivative of the given function at the indicated point. $$f(x)=x^{2}+4, a=1$$

In Exercises \(1-6,\) find \(d y / d x\). $$y=\frac{x^{3}}{3}-x$$