Understanding the Straight Chain Rule: Help Needed!

In summary, the individual is asking for help understanding a straight chain rule application, specifically for the problem D/dx (dy/dx)^2. They originally thought the answer would include 2 (dy/dx) (d2y/dx2) but after checking papers, realized it should be 2 (d2y/dx2). Additionally, they made a mistake in realizing the paper was differentiating by y not x.
  • #1
Mgarrettny
4
0
Can someone help me out with what I believe who.d be a straight chain rule application?

D/dx (dy/dx)^2

I would think, applying the chain rule, you get

2 (dy/dx) d/dx (dy/dx) = 2 (dy/dx) (d2y/dx2)

But, from the papers I checked, the (dy/dx) in the answer goes away, leaving just

2 (d2y/dx2)

What am I missing?
 
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  • #2
Can you rewrite your question in LaTex? I don't quite follow what you are saying.
 
  • #3
Mgarrettny said:
Can someone help me out with what I believe who.d be a straight chain rule application?

D/dx (dy/dx)^2

I would think, applying the chain rule, you get

2 (dy/dx) d/dx (dy/dx) = 2 (dy/dx) (d2y/dx2)

But, from the papers I checked, the (dy/dx) in the answer goes away, leaving just

2 (d2y/dx2)

What am I missing?

If you have referred correctly to the paper, the paper is wrong.
 
  • #4
Sorry everyone, ignore this.
 
  • #5
Thanks arildo, especially for the light speed reply. The paper was right, it was I who was wrong. I did not realize the paper was differentiating by y not x. Mea culpa.
 

Related to Understanding the Straight Chain Rule: Help Needed!

1. What is the straight chain rule in mathematics?

The straight chain rule, also known as the chain rule, is a mathematical rule used to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function.

2. Why is it important to understand the straight chain rule?

Understanding the straight chain rule is important because it allows us to find the derivative of more complex functions by breaking them down into simpler functions. This is especially useful in calculus and other branches of mathematics where derivatives are frequently used.

3. How do I apply the straight chain rule?

To apply the straight chain rule, you first need to identify the inner and outer functions of the composite function. Then, find the derivative of the outer function and the derivative of the inner function. Finally, multiply these two derivatives together to find the derivative of the composite function.

4. Can the straight chain rule be applied to functions with multiple variables?

Yes, the straight chain rule can be applied to functions with multiple variables. In this case, we use partial derivatives to find the derivative of the outer and inner functions and then multiply them together to find the derivative of the composite function.

5. Are there any common mistakes made when using the straight chain rule?

Yes, there are some common mistakes that can be made when using the straight chain rule. These include incorrectly identifying the inner and outer functions, miscalculating the derivatives, and forgetting to multiply the derivatives together. It is important to double check your work and practice using the rule to avoid these mistakes.

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