Find the 50th derivative of the function

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Homework Help Overview

The problem involves finding the derivatives of the function y = sin(3x), specifically the first five derivatives and a general rule for determining the 50th derivative. The subject area is calculus, focusing on differentiation and patterns in derivatives.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss identifying a pattern in the derivatives of the function, noting the signs and coefficients associated with each derivative. There is an emphasis on recognizing the cyclical nature of the derivatives of sine and cosine functions.

Discussion Status

Some participants have shared their attempts at identifying a pattern, while others have expressed a desire for clarification on the differentiation process. There is an indication that a productive direction is emerging, particularly in recognizing how to derive the 50th derivative based on established patterns.

Contextual Notes

Participants mention the urgency of the request and the need for clear steps to follow. There is also a reference to the problem being similar to finding patterns in other mathematical contexts, suggesting a broader exploration of derivative behavior.

Mathysics
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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:
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sorry it should be the 50th derivative
 


Mathysics said:

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 : )
 


i know it now...

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

thx for the help :)
 

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