Learning Materials
Features
Discover
Chapter 10: Problem 801
If \(f\) is an even function and \(f^{\prime}(x)\) is define than \(f^{\prime}(x)+f^{\prime}(-x)\) (a) 0 (b) \(<0\) \((\mathrm{c}) \neq 0\) \((\mathrm{d})>0\)
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
If \(\mathrm{y}=\mathrm{x}^{\mathrm{x}}\) and \(\left[\left(\mathrm{d}^{2} \mathrm{y}\right) /\left(\mathrm{d} \mathrm{x}^{2}\right)\right]-(\mathrm{y} / \mathrm{x})=(1 / \alpha) \cdot(\mathrm{dy} / \mathrm{d} \mathrm{x})^{2}\) then (a) \(\mathrm{x}^{\mathrm{y}}\) (b) \(x^{x}\) (c) \(\mathrm{y}^{\mathrm{x}}\) (d) \(x\)
If \(\mathrm{e}^{\mathrm{y}}=\left(\mathrm{e}^{2} / \mathrm{x}^{2}\right)\) and \(\left[\left(\mathrm{d}^{2} \mathrm{y}\right) /\left(\mathrm{d} \mathrm{x}^{2}\right)\right]=\left(\mathrm{A} / \mathrm{x}^{2}\right)\) the \(\mathrm{A}=\) (a) \(-2\) (b) \((1 / 2)\) (c) 2 (d) \((1 / 3)\)
For \((\mathrm{d} / \mathrm{dx}) \log \left|\mathrm{e}^{\mathrm{x}}[(\mathrm{x}-4) /(\mathrm{x}+4)]^{(3 / 4)}\right|\) at \(\mathrm{x}=5\) then \((\mathrm{dy} / \mathrm{d} \mathrm{x})\) \(\begin{array}{llll}\text { (a) }(5 / 3) & \text { (b) }(3 / 5) & \text { (c) }-(3 / 5) & \text { (d) }-(5 / 3)\end{array}\)
If \(\mathrm{y}=\tan ^{-1}\left[1 /\left(\mathrm{x}^{2}+\mathrm{x}+1\right)\right] \tan ^{-1}\left[1 /\left(\mathrm{x}^{2}+3 \mathrm{x}+3\right)\right]\) \(+\tan ^{-1}\left[1 /\left(\mathrm{x}^{2}+5 \mathrm{x}+7\right)\right] \ldots \ldots\) to \(\mathrm{n}\) terms then \((\mathrm{dy} / \mathrm{d} \mathrm{x})\) \(=\) (a) \(\left[1 /\left\\{1+(\mathrm{x}+\mathrm{n})^{2}\right\\}\right]+\left[1 /\left(1+\mathrm{x}^{2}\right)\right]\) (b) \(\left[1 /\left\\{1+(\mathrm{x}+\mathrm{n})^{2}\right\\}\right]-\left[1 /\left(1+\mathrm{x}^{2}\right)\right]\) (c) \(\left[2 /\left\\{1+(\mathrm{x}+\mathrm{n})^{2}\right\\}\right]+\left[1 /\left(1+\mathrm{x}^{2}\right)\right]\) (d) \(\sum \mathrm{n}\)
If \(\mathrm{y}=(1 / 3) \log \left[\\{\mathrm{x}+1\\} /\left\\{\mathrm{V}\left(\mathrm{x}^{2}+\mathrm{x}+1\right)\right\\}\right]+(1 / \sqrt{3}) \tan ^{-1}\) \([(2 x-1) /(\sqrt{3})]\) then \((d y / d x)=\) (a) \(\left[1 /\left(1+\mathrm{x}^{3}\right)\right]\) (b) \(\left[\left(x^{2}+x+1\right) /(x-1)\right]\) (c) \(\left[1 /\left(1-\mathrm{x}^{3}\right)\right]\) (d) none of these
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App