mathematical induction qn (1 Viewer)

[Masaken]

Use mathematical induction to prove that the nth derivative of y = cos x is y^n = cos(x+{[n*pi]/2}). (sorry, not able to ss the qn itself but the expression is in the attached ss of the working out)

Basically I got this question wrong and got stuck when I was attempting to redo it. I've attached the working out for the question, however I don't get it; in the first one, why is n = 1 true? Is it simply because the derivative of cos is -sin?



And in the second ss above, when I attempted the inductive step for n = k+1, while I did y=k^(n+1), I broke it apart and tried to do y^k * y^1; why did they do [y^k]^1? Wouldn't that just be y^k?? Thanks in advance

 

[Drongoski]

y = cos x means y'= -sin x = cos(x+pi/2)
For n=1


.: true for n=1

Suppose formula is true for n=k>=1


i.e. if true for n=k, then true also for the next one: n=k+1

Therefore ... blah ... blah ... blah ...

 

[mmmmmmmmaaaaaaa]

by log laws y^k * y^1 and (y^k)^1 and y^(k+1) are the same

 

[Antadhur123]

Serious question: Instead of taking the time to ask the whole of this forum, why not ask a friend or two for advice. It would save you a lot of time.

 

[Life'sHard]

Serious question: Instead of taking the time to ask the whole of this forum, why not ask a friend or two for advice. It would save you a lot of time.

Instead of taking the time to ask your friend, why not ask the forum for advice.

Also there are specialists here. That’s like asking why find a tutor for help when you can ask your friend. Sure your friend might know a thing or two but they definitely will not have the same insight as some of the people on this forum.

 

[Antadhur123]

Instead of taking the time to ask your friend, why not ask the forum for advice.

Also there are specialists here. That’s like asking why find a tutor for help when you can ask your friend. Sure your friend might know a thing or two but they definitely will not have the same insight as some of the people on this forum.

Because it takes longer for you to get a reply on this forum (if even an adequate/correct reply). It's not analogous to "Why find a tutor for help when you can ask your friend" because a tutor has a specific role which is to teach. I don't really mind tbh but I'm just saying efficiency wise, asking a small question like how do this question may not be worth the lengthy time you have to wait to get the answer.

 

[jimmysmith560]

At the end of the day, users are free to use BoS to seek assistance of any kind, as long as they do not breach forum rules. Users are different (understandably so), and whether an individual user may not be able to justify a particular thread being posted, others do, and this also means that the circumstances differ between users.

If you wish to continue this discussion, please do so in a different/new thread in the appropriate forum. Thanks.