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

In summary, the conversation is about the confusion and questions regarding a simple derivative, specifically the product rule and notation. The conclusion is that d(xf)/dx is equal to x(df/dx) + f(dx/dx) or x multiplied by the derivative of f with respect to x, and further simplification is not possible.
  • #1
LogicX
181
1
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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  • #2
No, that is x multiplied by the derivative of f, you cannot simplify more.
 
  • #3
x df/dx is the derivative of the function, f, with respect to, x, multiplied by x
 
  • #4
Is d(xf)/dx= x(df/dx) + f (dx/dx)= x (df/dx) + f ?

This was your original question. The answer is yes.
 

1. What is the meaning of the "d" in calculus notation?

The "d" in calculus notation typically represents a small change or infinitesimal change in a variable. For example, in the notation dx/dy, the "d" represents a small change in x with respect to a small change in y.

2. What does the notation f'(x) mean?

The notation f'(x) represents the derivative of a function f with respect to the variable x. It is also commonly read as "f prime of x."

3. What is the difference between dy/dx and d/dx?

The notation dy/dx represents the derivative of a function y with respect to the variable x, while d/dx represents the derivative of any function with respect to x. In other words, dy/dx is a specific type of derivative notation, while d/dx is a general notation for derivatives.

4. What does the notation ∫f(x)dx mean?

The notation ∫f(x)dx represents the integral of a function f with respect to the variable x. It is also commonly read as "the integral of f(x) with respect to x."

5. What is the purpose of using calculus notation?

Calculus notation is used to represent mathematical concepts and relationships in a concise and organized manner. It allows for precise communication and calculation of complex mathematical ideas and is essential in many scientific fields such as physics, engineering, and economics.

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