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
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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
 
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  • #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/
 
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  • #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.
 
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  • #5
still does not preview
 
  • #6
karush said:
still does not preview
Reload the page to enforce a rendering.
 
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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:
 
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  • #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!
 
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  • #11
valuable to know that ... mahalo
 

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

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.

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