# Is the derivative of 2x^2 = 4x or 8x?

Call me crazy, but I do recall the power rule of integration viz: f(x) = x^n, f(x)' = n*x^n-1. Therefore, it seems as though 2x^2 would have a derivative of 4x. Fine. So why have I encountered someone else claiming that it's 8x? WHAT?! Who's right?

Mark44
Mentor
Call me crazy, but I do recall the power rule of integration viz: f(x) = x^n, f(x)' = n*x^n-1.
Do you really mean ##n * x^n - 1##? That's what you wrote. As inline text, use parentheses -- n*x^(n - 1)

5P@N said:
Therefore, it seems as though 2x^2 would have a derivative of 4x.
Yes. ##d/dx(2x^2) = 4x##.
5P@N said:
Fine. So why have I encountered someone else claiming that it's 8x? WHAT?! Who's right?
Maybe they're working a different problem.

S.G. Janssens
So why have I encountered someone else claiming that it's 8x?
I can think of many reasons, but none of them involve mathematics.

I haven't yet applied Latex (I'm going to read the article after I finish reading this other long article on u-substitution - I'm really trying here), but what I mean is the super basic power rule of derivatives: f(x) = xn, f(x)' = nxn-1

S.G. Janssens
You are right, the other person must have a brain worm. Also, I would write ##f'(x)## instead of ##f(x)'##.

EDIT: Could you prove that the other has a brain worm?

Last edited:
And just for the record: I meant DERIVATION, not integration.

Mark44
Mentor
And just for the record: I meant DERIVATION, not integration.
Contrary to much popular opinion, the opposite of integration is differentiation, not derivation. You can derive the quadratic formula using the completion of squares technique, but you differentiate ##2x^2## to get the derivative, 4x. Yes, English is weird...

fresh_42
Mentor
Contrary to much popular opinion, the opposite of integration is differentiation, not derivation. You can derive the quadratic formula using the completion of squares technique, but you differentiate ##2x^2## to get the derivative, 4x. Yes, English is weird...
Thanks for clarifying. I sometimes get confused because the result of differentiation is a derivative (obeying the product rule) and the result of integration is an anti-derivative. Is that correct or am I still confusing terms?

Mark44
Mentor
Thanks for clarifying. I sometimes get confused because the result of differentiation is a derivative (obeying the product rule) and the result of integration is an anti-derivative. Is that correct or am I still confusing terms?
No, you have it right.

Erland