Problem 2
In Exercises \(1-8,\) use the given substitution and the Chain Rule to find \(d y / d x\) $$y=\sin (7-5 x), u=7-5 x$$
Problem 2
In Exercises \(1-6,\) find \(d y / d x\). $$y=\frac{x^{3}}{3}-x$$
Problem 2
In Exercises \(1-8,\) find the derivative of \(y\) with respect to the appropriate variable. $$y=\cos ^{-1}(1 / x)$$
Problem 2
(a) Write the area A of a circle as a function of the circumference C. (b) Find the (instantaneous) rate of change of the area A with respect to the circumference C. (c) Evaluate the rate of change of \(A\) at \(C=\pi\) and \(C=6 \pi\) (d) If \(C\) is measured in inches and \(A\) is measured in square inches, what units would be appropriate for \(d A / d C ?\)
Problem 2
In Exercises \(1-28\) , find \(d y / d x\) . Remember that you can use NDER to support your computations. $$y=e^{2 x}$$
Problem 2
In Exercises \(1-8,\) find \(d y / d x\). $$x^{3}+y^{3}=18 x y$$
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 \(1-8,\) find \(d y / d x\). $$y^{2}=\frac{x-1}{x+1}$$
Problem 3
(a) Write the area A of an equilateral triangle as a function of the side length s. (b) Find the (instantaneous) rate of change of the area A with respect to a side s. (c) Evaluate the rate of change of A at s " 2 and s " 10. (d) If \(s\) is measured in inches and \(A\) is measured in square inches, what units would be appropriate for \(d A / d s ?\)
