Chapter 2: Problem 21
In Exercises 3–24, use the rules of differentiation to find the derivative of the function. $$ y=x^{2}-\frac{1}{2} \cos x $$
Chapter 2: Problem 21
In Exercises 3–24, use the rules of differentiation to find the derivative of the function. $$ y=x^{2}-\frac{1}{2} \cos x $$
All the tools & learning materials you need for study success - in one app.
Get started for freeUsing Related Rates In Exercises \(1-4,\) assume that \(x\) and \(y\) are both differentiable functions of \(t\) and find the required values of \(d y / d t\) and \(d x / d t .\) $$ \begin{array}{rlrl}{y=\sqrt{x}} & {\text { (a) } \frac{d y}{d t} \text { when } x=4} & {} & {\frac{d x}{d t}=3} \\ {} & {\text { (b) } \frac{d x}{d t} \text { when } x=25} & {} & {\frac{d y}{d t}=2}\end{array} $$
Moving Point In Exercises \(5-8,\) a point is moving along the graph of the given function at the rate \(d x / d t .\) Find \(d y / d t\) for the given values of \(x .\) $$ \begin{array}{l}{y=\tan x ; \frac{d x}{d t}=3 \text { feet per second }} \\\ {\begin{array}{llll}{\text { (a) } x=-\frac{\pi}{3}} & {\text { (b) } x=-\frac{\pi}{4}} & {\text { (c) } x=0}\end{array}}\end{array} $$
Let \(f(x)=a_{1} \sin x+a_{2} \sin 2 x+\cdots+a_{n} \sin n x,\) where \(a_{1}, a_{2}, \ldots, a_{n}\) are real numbers and where \(n\) is a positive integer. Given that \(|f(x)| \leq|\sin x|\) for all real \(x,\) prove that \(\left|a_{1}+2 a_{2}+\cdots+n a_{n}\right| \leq 1\)
Tangent Lines Find equations of the tangent lines to the graph of \(f(x)=(x+1) /(x-1)\) that are parallel to the line \(2 y+x=6 .\) Then graph the function and the tangent lines.
True or False? In Exercises \(129-134\) , determine whether the statement is true or false. If is false, explain why or give an example that shows it is false. The second derivative represents the rate of change of the first derivative.
What do you think about this solution?
We value your feedback to improve our textbook solutions.