Help for Second Derivatives (1 Viewer)

alussovsky · Oct 27, 2018

Hi all! I'm having a lot of trouble with finding the second derivatives, with questions 12 c to f. It seems like normal product/chain/quotient rules don't work for these questions when trying to find second derivatives...? Or I'm just screwing it up really badly, lol

Also how to do 13...?

and thank you

InteGrand · Oct 28, 2018

alussovsky said:
Hi all! I'm having a lot of trouble with finding the second derivatives, with questions 12 c to f. It seems like normal product/chain/quotient rules don't work for these questions when trying to find second derivatives...? Or I'm just screwing it up really badly, lol

Also how to do 13...?

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and thank you

$\noindent What have been your attempts thus far? To find $y''$ in terms of $t$, first find $y'$ in terms of $t$ using $y'=\frac{dy/dt}{dx/dt}$. Then, we will have $y'' = \frac{dy'}{dx}= \frac{dy'}{dt}\frac{dt}{dx}$. (And make sure you remember how to find something like $\frac{dt}{dx}$!)$

$\noindent For Q13, calculate $y'$ and $y''$ from $y=x^a + x^{-b}$. Then sub. in expressions for $y,y',y''$ to the given equation that needs to be satisfied and group like terms. To find the $a$ and $b$, you'll want to \textsl{equate coefficients} so that $x^a$ and $x^{-b}$ on both sides of the equation have the same coefficient.$

alussovsky · Oct 28, 2018

Hi! I have managed to get the first derivatives of all of them but I'm stuck at getting the second ones. For example, the first derivative of c is -1/2t², which I managed to get, but if I change it to 1/2(t^-2) (which is the same thing... right?) and try to differentiate, I end up with -1/t³ while the answer is 1/2t³

(Also, uhhh, how do you get the letters and division to be in that formatting?)

InteGrand · Oct 28, 2018

alussovsky said:
Hi! I have managed to get the first derivatives of all of them but I'm stuck at getting the second ones. For example, the first derivative of c is -1/2t², which I managed to get, but if I change it to 1/2(t^-2) (which is the same thing... right?) and try to differentiate, I end up with -1/t³ while the answer is 1/2t³

(Also, uhhh, how do you get the letters and division to be in that formatting?)

$\noindent If you have the first derivative $y'=\frac{dy}{dx}$ in terms of $t$, to get the second derivative, you have to differentiate the first derivative $y'$ with respect to $t$ \emph{but then also \color{blue}\underline{multiply by $\frac{dt}{dx}$}}\color{black}. In other words, we have $\boxed{y'' = \frac{dy'}{dt}\color{blue}\times \frac{dt}{dx}\color{black}}$. This is due to the chain rule. Did you remember to multiply by $\frac{dt}{dx}$? (Remember also that to calculate $\frac{dt}{dx}$, it is equal to the reciprocal of $\frac{dx}{dt}$.)$

InteGrand · Oct 28, 2018

$\noindent To type mathematical formulas here, we use something known as \emph{\LaTeX}. To type maths formulas in $\LaTeX$ on these forums, you need to know how to write $\LaTeX$ formulas, and also use what are known as ``TeX tags'' when you type things into the message box. TeX tags are like this:$

[.tex][./tex]

$\noindent (Except do not type those red dots when using them. I used them here because otherwise you wouldn't actually be able to see the TeX tags.) For example, to type $y=x^{2}$, you would type$

Code:

[[B][COLOR="#FF0000"].[/COLOR][/B]tex] y = x^{2}[[B][COLOR="#FF0000"].[/COLOR][/B]/tex]

$\noindent without including those red dots. This will give you:$

$y=x^{2}$ .

$\noindent There are $\LaTeX$ codes for typing all sorts of mathematical expressions (such as typing $\backslash\texttt{frac\{\}\{\}}$ to get fractions etc.). Basically whenever you want to type a maths formula, you need to type the $\LaTeX$ code for that formula and place it between the TeX tags when writing your message. See also this link for some $\LaTeX$ help for this forum:$

http://community.boredofstudies.org/10/maths/234259/short-guide-latex.html.

$\noindent You can also use the following site to generate the $\LaTeX$ codes for mathematical expressions you desire, which can be copied and pasted into these message boxes (inside TeX tags), if you are unsure what the $\LaTeX$ code for something is or don't want to write it yourself:$

http://www.codecogs.com/latex/eqneditor.php.

$\noindent You can practice writing $\LaTeX$ codes and messages on this forum here:$

http://community.boredofstudies.org/3/non-school/333909/latex-testing-practice-3.html.

As another example (typing fractions), typing

Code:

[[B][COLOR="#FF0000"].[/COLOR][/B]tex] \frac{22}{7}[[B][COLOR="#FF0000"].[/COLOR][/B]/tex]

(without the red dots) will result in

$\frac{22}{7}$ .

alussovsky · Oct 28, 2018

InteGrand said:
$\noindent If you have the first derivative $y'=\frac{dy}{dx}$ in terms of $t$, to get the second derivative, you have to differentiate the first derivative $y'$ with respect to $t$ \emph{but then also \color{blue}\underline{multiply by $\frac{dt}{dx}$}}\color{black}. In other words, we have $\boxed{y'' = \frac{dy'}{dt}\color{blue}\times \frac{dt}{dx}\color{black}}$. This is due to the chain rule. Did you remember to multiply by $\frac{dt}{dx}$? (Remember also that to calculate $\frac{dt}{dx}$, it is equal to the reciprocal of $\frac{dx}{dt}$.)$

AAAHHH, SORRY, THAT WAS WHAT I FORGOT TO DO!! OH GEEZ-- Thank you so much for your help! Sorry for all that trouble... Thank you again for both the whole stupid mistake where I forgot to do the most obvious thing, and the coding!

Ace0804 · Oct 28, 2018

Could someone help me out, in finding the minimum acceleration

Help for Second Derivatives (1 Viewer)

alussovsky

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InteGrand

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alussovsky

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InteGrand

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InteGrand

Well-Known Member

alussovsky

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Ace0804

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