Differentiate ##f(x)=x\cos{x}+2\tan{x}: D/dx ##\tiny{2.4.2}##

In summary: I use AutoHotkey and an entire file of keyboard shortcuts to save time. E.g. Alt+I produces\begin{align*}\end{align*}with the cursor in the middle. Or \operatorname{} is Ctrl+o, again with the cursor at the right position. Similar for two dozen other shortcuts like Ctrl+u for \subseteq and Alt+u for \left.
  • #1
karush
Gold Member
MHB
3,269
5
Homework Statement
s8.2.4.2
Relevant Equations
product rule
##\tiny{2.4.2}##
Differentiate ##f(x)=x\cos{x}+2\tan{x}##
Product Rule ##[-x\sin{x}+\cos{x}]+[2\sec^2]\implies \cos{x}-x\sin{x}+2\sec^2x##
mostly just seeing how posting here works

typos maybe
suggestions
what forum do I go to for tikz stuff
 
Last edited:
  • Like
Likes vanhees71 and fresh_42
Physics news on Phys.org
  • #2
karush said:
Homework Statement:: s8.2.4.2
Relevant Equations:: product rule

##\tiny{2.4.2}##
Differentiate ##f(x)=x\cos{x}+2\tan{x}##
Product Rule ##[-x\sin{x}+\cos{x}]+[2\sec^2]\implies \cos{x}-x\sin{x}+2\sec^2x##
mostly just seeing how posting here works

typos maybe
suggestions
what forum do I go to for tikz stuff
The typos are the same. Otherwise, use ## instead of $ for inline LaTeX and $$ for extra lines.
Here is explained how you can type formulas on PF: https://www.physicsforums.com/help/latexhelp/
 
  • Like
Likes vanhees71 and karush
  • #3
this did not render latex or preview
 
  • #4
karush said:
this did not render latex or preview
See my previous post and the quotation where I changed the $ and the missing marks ## around \tiny.
 
  • Like
Likes vanhees71 and karush
  • #5
still does not preview
 
  • #6
karush said:
still does not preview
Reload the page to enforce a rendering.
 
  • Like
Likes vanhees71 and karush
  • #7
got it mahalo
however don't see solved option is title
 
  • #8
karush said:
however don't see solved option is title
We don't usually mark titles as Solved, since sometimes that status can change... :smile:
 
  • Like
Likes karush and topsquark
  • #9
##\dfrac{a}{b} \quad \frac{a}{b}##

ok I'm surprized you didn't mention \dfrac{}{} in the pdf which is the same as \displaystyle\frac{}{}
 
  • #10
karush said:
##\dfrac{a}{b} \quad \frac{a}{b}##

ok I'm surprized you didn't mention \dfrac{}{} in the pdf which is the same as \displaystyle\frac{}{}
It isn't my manual.

I use AutoHotkey and an entire file of keyboard shortcuts to save time. E.g. Alt+I produces
\begin{align*}

\end{align*}
with the cursor in the middle. Or \operatorname{} is Ctrl+o, again with the cursor at the right position. Similar for two dozen other shortcuts like Ctrl+u for \subseteq and Alt+u for \left. \dfrac{d}{d}\right|_{}

The advantage is that I can write Tex files as quickly as MathJax here.

Displaystyle is important if you want limits and sums within the text written with indexes positioned above and below instead of next to the symbol: ##\sum_{k=0}^n## versus ##\displaystyle{\sum_{k=0}^n}## and the same for ##\lim_{n \to \infty}## versus ##\displaystyle{\lim_{n \to \infty}}.## (Alt+- and Ctrl+-)

Edit: I also abuse AutoHotkey to kill that da** capslock!
 
Last edited:
  • Informative
  • Like
Likes karush, SammyS and berkeman
  • #11
valuable to know that ... mahalo
 

1. What is the derivative of the function f(x) = xcosx + 2tanx?

The derivative of f(x) is given by the formula f'(x) = (xcosx + 2tanx)' = x(-sinx) + cosx + 2(secx)^2.

2. How do you differentiate a function with both trigonometric and polynomial terms?

To differentiate a function with both trigonometric and polynomial terms, you can use the product rule, which states that the derivative of the product of two functions is equal to the first function times the derivative of the second function plus the second function times the derivative of the first function. In this case, the first function is xcosx and the second function is 2tanx.

3. Can the derivative of a function be simplified?

Yes, the derivative of a function can be simplified using algebraic rules and trigonometric identities. In the case of f(x) = xcosx + 2tanx, the derivative can be simplified to f'(x) = x(-sinx) + cosx + 2(secx)^2 = -xsinx + cosx + 2sec^2x.

4. What is the domain of the function f(x) = xcosx + 2tanx?

The domain of f(x) is all real numbers except for values of x that make the tangent function undefined, such as x = π/2 + nπ, where n is any integer. This is because the tangent function has vertical asymptotes at these values, making the function undefined.

5. How can the derivative of a function be used to find the slope of a tangent line?

The derivative of a function represents the slope of the tangent line at any given point on the function's graph. To find the slope of a tangent line at a specific point, simply plug in the x-coordinate of that point into the derivative function. For example, to find the slope of the tangent line at x = 1 for f(x) = xcosx + 2tanx, plug in x = 1 into the derivative f'(x) = -xsinx + cosx + 2sec^2x to get the slope of the tangent line at that point.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
346
  • Calculus and Beyond Homework Help
Replies
3
Views
795
  • Calculus and Beyond Homework Help
Replies
6
Views
760
  • Calculus and Beyond Homework Help
Replies
6
Views
952
  • Calculus and Beyond Homework Help
Replies
21
Views
840
  • Calculus and Beyond Homework Help
Replies
18
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
799
  • Calculus and Beyond Homework Help
Replies
1
Views
828
  • Calculus and Beyond Homework Help
Replies
22
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
Back
Top