Implicit Differentiation with Sin

In summary, the conversation is about a user receiving feedback on their use of the product rule when differentiating xy^2, and realizing their mistake. They then correct their mistake and receive confirmation that their work is correct.
  • #1
Pondera
13
0

Homework Statement


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Homework Equations





The Attempt at a Solution


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  • #2
It looks like you're not applying the product rule properly when differentiating xy^2. d(xy^2) = y^2 + 2xyy'
 
  • #3
I wasn't using the product rule at all. Thank you for that! Haha.

I tried it again and got:
1181answer2.jpg


Line by line:
7= cos(xy^2)(y^2+2xyy')
7/ cos(xy^2) = (y^2+2xyy')
7/ cos(xy^2) - y^2 = 2xyy'
(7/ cos(xy^2) - y^2)(2xy) = y'
 
  • #4
On your last step, why are you multiplying by 2xy?...Shouldn't you be dividing instead?:wink:
 
  • #5
Yeah, it should be divided by our multiplied by (1/2xy). I'm not sure why I did that. :P

The rest of it looks okay though?
 
  • #6
the rest looks fine :smile:
 
  • #7
WOOO! It was right! Thank you very much, jgens and gabba.
 

1. What is implicit differentiation with sin?

Implicit differentiation with sin is a mathematical technique used to find the derivative of a function that contains both an independent variable and the trigonometric function sine (sin). It is commonly used in calculus to solve complex equations involving trigonometric functions.

2. How is implicit differentiation with sin different from regular differentiation?

Regular differentiation involves finding the derivative of a function with a single independent variable. Implicit differentiation with sin, on the other hand, deals with functions that have both an independent variable and the trigonometric function sine (sin).

3. What is the process of implicit differentiation with sin?

The process of implicit differentiation with sin involves treating the sine function as if it were a regular variable, and using the chain rule to differentiate it. The rest of the function is then differentiated as usual. The final result will be an expression containing both the derivative of the original function and the derivative of the sine function.

4. What are some common applications of implicit differentiation with sin?

Implicit differentiation with sin is commonly used in physics and engineering, particularly in the study of oscillatory motion and wave phenomena. It is also used in economics and finance to model periodic changes in market trends.

5. Are there any limitations to using implicit differentiation with sin?

While implicit differentiation with sin is a powerful technique, it can only be applied to functions that contain the sine function. It cannot be used with other trigonometric functions, such as cosine or tangent, or with any other types of functions. Additionally, it is important to check for extraneous solutions when using implicit differentiation with sin, as it may yield multiple solutions that do not satisfy the original equation.

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