Problem 3
In Exercises \(1-6,\) find \(d y / d x\). $$y=2 x+1$$
Problem 3
In Exercises \(1-8,\) find the derivative of \(y\) with respect to the appropriate variable. $$y=\sin ^{-1} \sqrt{2} t$$
Problem 3
In Exercises \(1-10,\) find \(d y / d x\) . Use your grapher to support your analysis if you are unsure of your answer. $$y=\frac{1}{x}+5 \sin x$$
Problem 3
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. $$f(x)=3-x^{2}, a=-1$$
Problem 4
A square of side length s is inscribed in a circle of radius r. (a) Write the area A of the square as a function of the radius r of the circle. (b) Find the (instantaneous) rate of change of the area A with respect to the radius r of the circle. (c) Evaluate the rate of change of \(A\) at \(r=1\) and \(r=8\) (d) If \(r\) is measured in inches and \(A\) is measured in square inches, what units would be appropriate for \(d A / d r ?\)
Problem 4
In Exercises \(1-6,\) find \(d y / d x\). $$y=x^{2}+x+1$$
Problem 4
In Exercises \(1-8,\) use the given substitution and the Chain Rule to find \(d y / d x\) $$y=\tan \left(2 x-x^{3}\right), u=2 x-x^{3}$$
Problem 4
In Exercises \(1-10,\) find \(d y / d x\) . Use your grapher to support your analysis if you are unsure of your answer. $$y=x \sec x$$
Problem 4
In Exercises \(1-8,\) find the derivative of \(y\) with respect to the appropriate variable. $$y=\sin ^{-1}(1-t)$$
Problem 4
In Exercises \(1-8,\) find \(d y / d x\). $$x^{2}=\frac{x-y}{x+y}$$
