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clara1223
 one year ago
find f''(x) of f(x)=5cos(x^3)
clara1223
 one year ago
find f''(x) of f(x)=5cos(x^3)

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clara1223
 one year ago
Best ResponseYou've already chosen the best response.0\[f''(x)\] of \[f(x)=5\cos(x ^{3})\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Second derivative? Oh boy that'll be a bit of a doozy :o

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Did you find \(\large\rm f'(x)\) yet?

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure what to do with the x^3 inside

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3So you expect that it should give you `something like this`\[\large\rm \frac{d}{dx}5\cos(x^3)=5\sin(x^3)\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3But chain rule tells us to multiply by the derivative of the inner function.\[\large\rm \frac{d}{dx}5\cos(x^3)=5\sin(x^3)\cdot\color{royalblue}{(x^3)'}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3\[\large\rm \frac{d}{dx}5\cos(x^3)=5\sin(x^3)\cdot\color{orangered}{(3x^2)}\]Ya?

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0ya so we have \[15x ^{2}\sin(x ^{3})\] correct?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Looks good. Now things get a little more complicated. Looks like product rule from here, ya?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Here is how you would "set it up"\[\large\rm \frac{d}{dx}15x^2 \sin(x^3)=\color{royalblue}{(15x^2)'}\sin(x^3)15x^3\color{royalblue}{\left(\sin(x^3)\right)'}\]And you need to differentiate the blue parts.

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0i know that (15x^2)' is 30x but what is (sin(x^3))'?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3You should be able to do this one :) We just figured out what (cos(x^3))' is. This one is very very similar.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Claraaaaaaaaaaa! Gotta learn that chain rule!! MOAR PRACTICE! :)

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0OK so \[(\sin(x ^{3}))'=3x ^{2}\cos(x ^{3})\] yes?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3\[\large\rm \frac{d}{dx}15x^2 \sin(x^3)=\color{royalblue}{(15x^2)'}\sin(x^3)15x^3\color{royalblue}{\left(\sin(x^3)\right)'}\] \[\large\rm \frac{d}{dx}15x^2 \sin(x^3)=\color{orangered}{(30x)}\sin(x^3)15x^3\color{orangered}{\left(3x^2\cos(x^3)\right)}\]And then maybe combine things a lil bit.

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0\[30x \sin (x ^{3})45x ^{5}\cos(x ^{3})\] yes?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Woops! I made a boo boo somewhere!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3When I did the setup:\[\large\rm \frac{d}{dx}\left[15x^2 \sin(x^3)\right]=\color{royalblue}{(15x^2)'}\sin(x^3)\color{red}{15x^3}\color{royalblue}{\left(\sin(x^3)\right)'}\]Do you see anything wrong with this red part?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0zepdrix how do you get those colors for your latex equations?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dont mean to distract but I am just curious

ShadowLegendX
 one year ago
Best ResponseYou've already chosen the best response.0@PlasmaFuzer Read a LaTeX tutorial?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3The formatting language is LaTex You can google it and find out a lot of cool little features :) \color{specific color goes here}{your math goes here} for color

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3example: \color{red}{x^2} you would put this manually into the equation tool \(\color{red}{x^2}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ahh cool thank you... yea I use latex but never with colors but that is handy I will try and use it :D

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0@zepdrix I don't see anything wrong with the red part. When I do the product rule I get the same thing... What am I missing?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3@PlasmaFuzer Another cool thing you can do is: Right click someone's math code > Show Math As > Tex Commands and that will give you a pop up box of how I/someone entered it into the equation tool.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3It was a 15x^2, ya? Not 15x^3. I musta misclicked the power lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nice!!! thank you again :D :D anyways Ill stop distracting sorry clara cya both later

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0still relatively new to site... figuring things out

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0Oh! I got 15x^2, didn't even notice

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3So after differentiating, I should've had,\[\large\rm \frac{d}{dx}15x^2 \sin(x^3)=\color{orangered}{(30x)}\sin(x^3)15x^2\color{orangered}{\left(3x^2\cos(x^3)\right)}\]So we don't end up with a 5th power over there, ya? :)

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0\[30x \sin (x ^{3})45x ^{4}\cos (x ^{3})\] right? because when you multiply powers you add them?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3sec :) just double checking our work really quick

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0I just multiplied the 15x^2 and the 3x^2 in front of the cos to get 45x^4

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0That's the most simplified it's gonna get right?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3You could pull an x out of each term, but again, unnecessary :) Ya that's a good final answer.

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0Thank You!! you have been so helpful. I have 3 more questions tonight, hope you can help :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Calc is so much fun isn't it claire bear? :O
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