A community for students.
Here's the question you clicked on:
 0 viewing
Carissa15
 one year ago
Hi, I have a few derivative problems if anyone is able to help please?
Carissa15
 one year ago
Hi, I have a few derivative problems if anyone is able to help please?

This Question is Closed

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438832647688:dw

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.11) \[f(x)=\tan(x^3)\] I have then used the chain rule as follows (dx of outside) x (inside) x (derivative of inside)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4but we're just taking derivatives, not antiderivatives where usub thrives. o_O

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1Which I get\[=\sec(x^3) * 3x^2 \]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4isn't derivative of tan (x) sec^2x though?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4the derivative of x^3 is correct.. it does become 3x^2 and is written outside

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1So my method is correct but should be \[f \prime (x)=3x^2 \sec^2(x^3)\]?

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1awesome, thank you. I have a couple more but not sure where to start as they include \[\ln and \]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4trig derivatives sin (x) > cos(x) cos (x) > sin(x) tan (x) > sec^2(x) csc(x)  > csc(x)cot(x) sec(x) > secxtanx cot(x) = csc^2x

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4yes that table needs to be memorized just like all the derivative rules out there xX!

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1do you know what the rules are for e? another question is \[f(x)=e^xsinx\]

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1I thought it would be \[f \prime (x)=e \cos(x)\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4yeah... usually for e^x the exponent part for the e is left alone so for example the derivative of e^x is just e^x due to the fact that the derivative of x is 1, but nobody writes the 1 so derivative of x is one , but the exponent part that's attached to the e stays e^{x}(1)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4another example dw:1438833198807:dw

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4the derivative of x^2 is written in front of the e but the exponent part where x^2 stays is left alone

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1Oh ok, sorry just read your response. Great thanks. So in the second question it is only the sin to cos that changes?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4yes because we are using product rule on that one \[\LARGE f(x)=e^xsinx\] \[\LARGE f'(x)=e^x(cos(x))+sin(x)e^{x}\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4and the derivative of that x is just one so nothing drastic happens. . .

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4I left the e^x alone first and took the derivative of sinx + I left sin x alone and took the derivative of e^x derivative of e^x in that case is just e^x(1) or just written as e^x

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1great thank you, could it also be\[e^x(\cos(x))+e^x(\sin(x))\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4yeah... we could factor the e^x to make it nicer, but it's fine the way it is.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4order doesn't really matter that much.

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1cool, makes sense :) Thanks

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1I also have \[f(x)=\frac{ \ln x }{ x }\] I know that the dx of \[\ln (x)\] is \[\frac{ 1 }{ x }\] but not sure what to then do about the x underneath?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4the derivative of x is one so the derivative of ln(x) is just written as 1/x

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4maybe quotient rule will work if we had to do \[\LARGE f(x)=\frac{ \ln x }{ x } \]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4so the bottom gets squared then leave the second part (The denominator x alone) deal with ln x the derivative of ln x is 1/x(1) but again since the derivative of x is just 1 we don't have to write that extra stuff.. just 1/x will be good enough.  leave the first part (the numerator ln x alone ) deal with the x the derivative of x is just 1

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4\[\LARGE f(x)=\frac{ \ln x }{ x } \] \[\LARGE f'(x)=\frac{ (x) \frac{1}{x} ln(x)(1) }{ x^2 } \] \[\LARGE f'(x)=\frac{\frac{x}{x} ln(x)(1) }{ x^2 } \] \[\LARGE f'(x)=\frac{1 ln(x) }{ x^2 } \]

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1(f’ g − g’ f )/g2 so I get\[\frac{ 1 }{ x } * x 1 * lnx\] over x^2

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4yeah we can cancel the x/x and we don't have to write the 1 for the lnx

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1So for \[f(x)=e^\sin x\]

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1as the sin x is an exponent of e it remains untouched?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4\[\LARGE f(x) = e^{sinx}\] like this?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4so take the derivative of sin(x) and put it in front of the e. leave the exponent part of e which is at e^{sinx} alone.

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1oh, yeah i forgot that we still multiply but do not change the original as well. Cool. Thank you. I have one more question.

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1\[f(x)=\ln(\sin^2x)\]

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1would it be\[\frac{ 1 }{ x } *\cos^2\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4wow... ok to make it easier we can rewrite that \[\LARGE f(x)=\ln((sinx)^2)\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4then we know that since we have a log it will be 1/(sinx)^2 but then we have to take the derivative of (sinx)^2

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4\[\LARGE f(x)=\ln((sinx)^2) \rightarrow \frac{1}{(sinx)^2}2(sinx)\cos(x)\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4\[\LARGE f'(x) = \frac{2\cos(x)}{\sin(x)}\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4I had one sin x on the top but 2 sin x 's on the bottom.. one of them cancels..

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1great, that makes much more sense now.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4yeah but here's the thing.. .when I checked on wolfram it used a trig identity see that 2sinxcosx ? sin2x = 2sinxcosx

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4\[\LARGE f'(x)=\ln((sinx)^2) \rightarrow \frac{1}{(sinx)^2}\sin2x\] interesting... we need trig identities. according to mr.wolfram the derivative is 2 cot(x)

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1hmmm. I got this on mathway 2csc2(x)cos(x)sin(x)

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1but not sure how it got there....

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4ok hold up let's take the (sinx)^2 out for a bit let let a = (sinx)^2 so we just have ln a for now

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4\[\LARGE f(x) = \ln(a) \rightarrow f'(x) = \frac{1}{a}\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4so if we have \[\LARGE a = (sinx)^2 \] \[\LARGE a' = 2(sinx)(cosx) \]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4however there is a trig identity so that 2sinxcosx is replaced with sin2x

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4OMG. ok let's use log rules on this beast.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4exponent rule is needed so... \[\LARGE f(x)=\ln((sinx)^2)\] becomes \[\LARGE f(x)=2\ln((sinx))\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4and then use product rule... YEAH I SEE IT NOW!

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4we just need one part of the product rule because 2 is a constant and all constants have the derivative of 0

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4\[\LARGE f(x)=2\ln((sinx)) \] \[\LARGE f'(x)=2(\frac{1}{sinx})(cosx)+ \ln(sinx)(0)\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4\[\LARGE f'(x)=2(\frac{cosx}{sinx}) \rightarrow 2\cot(x) \]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4sh.it I had that earlier ... just forgot to take the identity of cosx/sinx

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.412 minutes ago I had this \[\LARGE f'(x) = \frac{2\cos(x)}{\sin(x)} \]

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1I have not come across trig identities yet, another set of rules for specific trig functions?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4trigonometry comes before calculus... so eventually by now all the trig identities have to be mastered and memorized... I just overlooked that one part.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4\[\LARGE f'(x) = 2 \cot(x) \]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4so I didn't have to use sin2x = 2sinx cosx after all... just had to cancel one of the sinx and then use cosx/sinx = cotx and that's what wolfram got too.

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1awesome, I will have a closer look at trigonometry. Thank you so much for all of your help. Has been amazing!

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.4yeah... it wasn't too bad... except for the last one when I overlooked something... XD! and then taking the identity of 2sinxcosx made it worse. XD

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1All good, was so lost without your help. Thanks again, I will close this now :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.