What is the product rule for finding a derivative in calculus?

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Discussion Overview

The discussion revolves around the product rule for finding derivatives in calculus, specifically addressing the expression d(xf)/dx and its interpretation. Participants explore the notation and the application of the product rule in this context.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant expresses confusion about the product rule and the notation involved in differentiating the expression d(xf)/dx.
  • Another participant clarifies that x df/dx represents x multiplied by the derivative of f with respect to x, indicating that it cannot be simplified further.
  • A third participant reiterates that x df/dx is indeed the derivative of f with respect to x, multiplied by x.
  • A later reply confirms that the original expression d(xf)/dx equals x(df/dx) + f, affirming the application of the product rule.

Areas of Agreement / Disagreement

Participants generally agree on the application of the product rule and the interpretation of the notation, with no significant disagreement noted.

Contextual Notes

Some participants express uncertainty about their understanding of calculus notation, which may affect their interpretations.

LogicX
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It's been a while since I've done calculus and now a simple derivative is stumping me.

This is the issue: d(xf)/dx= ?

This is just the product rule, so I think: x(df/dx) + f (dx/dx)= x (df/dx) + f

But I'm afraid that I don't even understand my own notation anymore (how embarrassing)...

if I had a derivative like x (d/dx), would this just be the derivative of x, i.e. 1? So what does x df/dx mean? You can't simplify that anymore, right? Maybe I just need to go reread my calc 1 textbook..
 
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No, that is x multiplied by the derivative of f, you cannot simplify more.
 
x df/dx is the derivative of the function, f, with respect to, x, multiplied by x
 
Is d(xf)/dx= x(df/dx) + f (dx/dx)= x (df/dx) + f ?

This was your original question. The answer is yes.
 

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