A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing

This Question is Closed

Sujay
 2 years ago
Best ResponseYou've already chosen the best response.0When you say y prime, do you mean the derivative?

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1Please someone help me I m stuck and its due tomorrow

goformit100
 2 years ago
Best ResponseYou've already chosen the best response.0Yo Yo, diffrentiate on both sides...

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1These are kind of new problems to me if you dont mind can you teach me and help me solving them?

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1can we go step by step?

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1you want to go by steps sure will do

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1at the end i will show u how u can work such equation in ur head, without paper and pen

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1Thanks to both of you Sujay and Mathsmind :)

Sujay
 2 years ago
Best ResponseYou've already chosen the best response.0Original Equation:\[y=\sin^21(2x3)?\]

Sujay
 2 years ago
Best ResponseYou've already chosen the best response.0I want to make sure my original is correct

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[y=\sin^{1}(2x^3)\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1please confirm is this what u r asking for?

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1ok let me write down the equation here. Its \[y=\sin^{1} (2x ^{3})\]

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1yeah I m here sorry I was just writing that equation down

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1yeah you are right Mathmind

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1ok there are 2 main ways to solve this problem at ur level

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1is there any easy way bcoz I have 4 more to do after this one so I need to understand the whole thing my professor method was too hard

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1differentiate both sides

Sujay
 2 years ago
Best ResponseYou've already chosen the best response.0Original:\[\sin^{1} (2x^3)\] Use the chain rule: Derivative out the outside times the derivative of the inside. \[\sin(2x^3)[\cos(2x^3)](6x^2) \] and there you have it, now simplify.

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[cosy \frac{ dy }{ dx }=1\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ dy }{ dx }=\frac{ 1 }{ cosy }\]

Sujay
 2 years ago
Best ResponseYou've already chosen the best response.0Apparently my answer is wrong, terribly sorry, I'll see where I went wrong :(.

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sin^2y+\cos^2y=1\]

Sujay
 2 years ago
Best ResponseYou've already chosen the best response.0Oh yes, my sine needs to be raised to a negative 2

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1be patient both of u i will solve it in different way and u pick up the easiest method ok, all the best

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[cosy=\pm \sqrt{1\sin^2y}\]

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1thank u so much Mathsmind and its ok Sujay

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ dy }{ dx } = \frac{ 1 }{ \sqrt{1\sin^2y} }\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1now remember our rearrangement\[\sin(y)=x\] so substitute that in the above equation

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ dy }{ dx } = \frac{ 1 }{ \sqrt{1x^2} }\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1now this is the general derivative of arcsin or sin inverse ok

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1now if you follow the same steps for\[y = \sin^{1}(2x^3)\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ dy }{ dx } = \frac{ 6x^2 }{ \sqrt{14x^6} }\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1and that's is your final answer achieved using the chain rule

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1let me prove that for you

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1ok plzz if you can do that

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1step One:\[2x^3=siny\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1step two: differentiate both sides

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[6x^2=\frac{ dy }{ dx }cosy\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1step three : rearrange the differential equation

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ dy }{ dx}=\frac{ 6x^2 }{ cosy }\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1step four: recall that \[cosy=\pm \sqrt{1\sin^2y}\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1step five: substitute cosy in the differential equation \[\frac{ dy }{ dx}=\frac{ 6x^2 }{ \sqrt{1\sin^2y} }\]

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1wow I am liking this method better than before

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1step six: recall\[siny=2x^3s\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1Step seven: substitute siny in the last deferential

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1what number is that under the power of 3?

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1that is a mistake an s

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1sorry i will do it again

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1step seven : substitute step 6 in step 5

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ dy }{ dx}=\frac{ 6x^2 }{ \sqrt{1(2x^3)^2} }\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1finally step eight : simplify

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ dy }{ dx}=\frac{ 6x^2 }{ \sqrt{14x^6} }\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1and this concludes our proof good luck

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1are you there? am sorry my computer is slow today

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1oh wow you explained really good thanks :)

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1so i deserve a medal then hehehe

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1Now I have to work on 4 more of these huh lets see how am I going to do it.

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1ok if you do those 4 by yourself i will give you a medal, does that sound fair?

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1you can use the triangle method as well to solve this

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1if you dont mind can I just step by step show you how to do that?

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1how am i gonna give u a medal then ! hehehe

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1oh yeah sorry i forgot hehe

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1u better not make one mistake

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1ohhh hmmm I am not sure about that but I m doing it

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1there is another method using Taylor's series

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1my professor also gave us the formula like for that equation the formula for \[\sin^{1} is 1/\sqrt{1u ^{2}}timesdu\]

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1yes that is the method of substitution which i see it as a lazy method

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.1but if u are used to that method then go for it, as soon as u get the right answer who cares, you know!

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.1the answer that I m getting is weird
Ask your own question
Ask a QuestionFind 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.