Derivative of a function, Is my answer correct?

Click For Summary

Homework Help Overview

The discussion revolves around finding the derivative of the function y = e^(9Θ)sin(8Θ). Participants are examining the correctness of a proposed solution and exploring the implications of different interpretations of the function's structure.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to differentiate the function and are questioning the presence of a missing factor in the derivative. There is also a discussion about the correct interpretation of the function's form, whether it is a product of two functions or a composition.

Discussion Status

The conversation is active, with participants providing insights and corrections regarding the differentiation process. Some guidance has been offered regarding the presence of an additional factor when differentiating the exponential part of the function.

Contextual Notes

There is mention of a potential misunderstanding regarding the function's structure, which may affect the differentiation approach. Participants are also reflecting on the implications of their interpretations and the resulting derivatives.

neutron star
Messages
78
Reaction score
1

Homework Statement


y=e^9Θsin(8Θ)


Homework Equations





The Attempt at a Solution


dy/dΘ=e^9Θ(sin(8Θ)+8cos(8Θ))
 
Physics news on Phys.org
[Edit] I didn't catch the missing 9; sorry about that.
 
Last edited:
is that (using t for theta)

y=e^(9t.sin(8t)) or y=(e^(9t)).sin(8t)?
 
Ugh, it said incorrect...
 
if it is
y=(e^(9t)).sin(8t)

i think you should get an extra factor of 9
y'=(e^(9t)).(9sin(8t)+ 8cos(8t))
 
Lanedance is right, you get that factor of 9 when taking the exponential derivative.
 

Similar threads

Area of Polar Curve: Find the Area Enclosed by r=2+sin(4θ)
  • · Replies 5 ·
Replies
5
Views
2K
Why do you get the area of a whole circle when you integrate
  • · Replies 21 ·
Replies
21
Views
3K
Why Does Trig Substitution Yield Different Integral Results?
  • · Replies 3 ·
Replies
3
Views
2K
Deriving the formula for arc length of a polar function
  • · Replies 4 ·
Replies
4
Views
2K
Is this the correct general solution of the given PDE?
  • · Replies 12 ·
Replies
12
Views
2K
Are these the correct expressions for ## dF/dy' ##?
  • · Replies 4 ·
Replies
4
Views
1K
Trigonometric Substitution Problem w/ Sin Substitution
  • · Replies 2 ·
Replies
2
Views
2K
Simple derivative of exponential function
  • · Replies 3 ·
Replies
3
Views
1K
How do we write a sinusoidal solution to a 2nd order DE as a sum of exponentials raised to complex roots?
  • · Replies 2 ·
Replies
2
Views
3K
The first and second derivatives at various points on a drawn graph
  • · Replies 22 ·
Replies
22
Views
3K