Find the 50th derivative of the function

[Mathysics]

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

 

[Mathysics]

sorry it should be the 50th derivative

 

[LareeRudi]

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 : )

 

[Mathysics]

i know it now...

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

thx for the help :)