Chapter 2: Problem 21
Finding a Derivative In Exercises \(7-34,\) find the derivative of the function. $$ y=\frac{1}{\sqrt{3 x+5}} $$
Chapter 2: Problem 21
Finding a Derivative In Exercises \(7-34,\) find the derivative of the function. $$ y=\frac{1}{\sqrt{3 x+5}} $$
All the tools & learning materials you need for study success - in one app.
Get started for freeThink About It Let \(f\) and \(g\) be functions whose first and second derivatives exist on an interval I. Which of the following formulas is (are) true? (a) \(f g^{\prime \prime}-f^{\prime \prime} g=\left(f g^{\prime}-f^{\prime} g\right)^{\prime} \quad\) (b) \(f g^{\prime \prime}+f^{\prime \prime} g=(f g)^{\prime \prime}\)
Differential Equations In Exercises \(125-128\) , verify that the function satisfies the differential equation. $$ \text{Function} \quad \text{Differential Equation} $$ $$ y=\frac{1}{x}, x>0 \quad x^{3} y^{\prime \prime}+2 x^{2} y^{\prime}=0 $$
Using 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 \(x .\) $$ \begin{array}{l}{y=\cos x ; \frac{d x}{d t}=4 \text { centimeters per second }} \\ {\begin{array}{llll}{\text { (a) } x=\frac{\pi}{6}} & {\text { (b) } x=\frac{\pi}{4}} & {\text { (c) } x=\frac{\pi}{3}}\end{array}}\end{array} $$
Determining Differentiability In Exercises \(75-80\) , describe the \(x\) -values at which \(f\) is differentiable. $$ f(x)=\sqrt{x-1} $$
What do you think about this solution?
We value your feedback to improve our textbook solutions.