Derivative of trigonometric functions

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Homework Help Overview

The discussion revolves around finding the derivative of the product of two trigonometric functions, specifically y = sin(4x) cos(3x). Participants are exploring the application of the product rule and the chain rule in this context.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the derivatives of the individual functions f(x) = sin(4x) and g(x) = cos(3x), questioning the correctness of the derivatives calculated. There is also exploration of whether sin(4x) can be expressed differently and inquiries about the chain rule.

Discussion Status

The discussion is active, with participants verifying each other's calculations and suggesting further simplifications. Some guidance has been provided regarding the derivatives, but there is no explicit consensus on the final form of the answer or its simplification.

Contextual Notes

Participants are considering the implications of rewriting sin(4x) and the potential need for graphing to understand the functions better. There is an emphasis on ensuring the correct application of differentiation rules.

fr33pl4gu3
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y = sin( 4 x ) cos( 3 x )

f(x) = sin4x
g(x) = cos3x
f'(x) = cos4x
g'(x) = -sin3x

And by using the product rule, i'll get:

cos4x(cos3x) - sin4x(sin3x)

Is the answer correct or can be simplify again??
 
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Check the f'(x) and g'(x). Are you missing something?
 
sin4x can be written in this way (4(sin x)) or not?
 
Last edited:
Is it

f'(x)=4cos(4x)

??
 
Last edited:
Yes :smile:
And the other?
 
so the answer would be

4cos4x(cos3x) -3 sin4x(sin3x)

Correct??
 
Yes.
 
can my last answer be simplify one more step?
 
  • #10
Not any that I can think of. It can be re-arranged. Do you have a target answer?
 
  • #11
fr33pl4gu3 said:
sin4x can be written in this way (4(sin x)) or not?
Try to draw the graphs for y= 4 sinx and y=sin4x for x= 0,30,45,60,90 degrees etc. and see for yourself.
 

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