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

[LogicX]

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..

 

[Tarantinism]

No, that is x multiplied by the derivative of f, you cannot simplify more.

 

[rollcast]

x df/dx is the derivative of the function, f, with respect to, x, multiplied by x

 

[alan2]

Is d(xf)/dx= x(df/dx) + f (dx/dx)= x (df/dx) + f ?

This was your original question. The answer is yes.