Find the 50th derivative of the function

  • Thread starter Mathysics
  • Start date
  • #1
Mathysics
37
0

Homework Statement


Find the first, second, third, fourth, fifth derivatives of the function y = sin 3x.

Find a rule that can help to find the 50th derivative of the function.

It's urgent!

Homework Equations


y= sin x y= cos x
y' = cos x y' = -sin x

y= sin ax y= cos ax
y' = a sin cos ax y' = -a sin ax


The Attempt at a Solution


My attempt to the question: y = -a^n sin ax for even
y = a^n cos ax for odd

Plz show steps so that i can follow, cheers
 
Last edited:

Answers and Replies

  • #2
Mathysics
37
0


sorry it should be the 50th derivative
 
  • #3
LareeRudi
34
0


Homework Statement


Find the first, second, third, fourth, fifth derivatives of the function y = sin 3x.

Find a rule that can help to find the 50th derivative of the function.

It's urgent!

Homework Equations


y= sin x y= cos x
y' = cos x y' = -sin x

y= sin ax y= cos ax
y' = a sin cos ax y' = -a sin ax


The Attempt at a Solution


My attempt to the question: y = -a^n sin ax for even
y = a^n cos ax for odd

Plz show steps so that i can follow, cheers
this to me is like a "puzle"; like the problem "find i^15" you find a pattern w/o having to go the whole way. Same here.

So you see the FIRST diff is pos and has the coeff of 3^1 and has "cos" in it
The SECOND diff is neg, coeff is 3^2 and has "sin" in it
The THIRD is neg, coeff is 3^3 and has "cos" in it
The FOURTH is pos, coeff is 3^4 and has "sin" in it.............. ummmmm, can you see what the FORTY EIGHTH is now? then so easy to go to the 49th and 50th from there.

Trying hard NOT to give you the ANSWER..... AND............ apologies if my differentiation is wrong.... I'm giving you a pattern to go by........ I think diff of sin3x is 3cos3x and then diff of cos3s is -3sin3x?????????? if wrong, FIX that part...... I'm trying to show you a PATTERN.

Good luck,

LarryR : )
 
  • #4
Mathysics
37
0


i know it now...

is (-1)^n/2 x a^n cos ax (for even)

thx for the help :)
 

Suggested for: Find the 50th derivative of the function

  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
4
Views
1K
Replies
2
Views
1K
Replies
4
Views
3K
Replies
4
Views
15K
  • Last Post
Replies
7
Views
838
Replies
11
Views
3K
Replies
19
Views
3K
Top