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

1. Jan 5, 2016

### 5P@N

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?

2. Jan 5, 2016

### Staff: Mentor

Do you really mean $n * x^n - 1$? That's what you wrote. As inline text, use parentheses -- n*x^(n - 1)

Yes. $d/dx(2x^2) = 4x$.
Maybe they're working a different problem.

3. Jan 5, 2016

### Krylov

I can think of many reasons, but none of them involve mathematics.

4. Jan 5, 2016

### 5P@N

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

5. Jan 5, 2016

### Krylov

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: Jan 5, 2016
6. Jan 5, 2016

### 5P@N

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

7. Jan 6, 2016

### Staff: 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...

8. Jan 6, 2016

### Staff: 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?

9. Jan 6, 2016

### Staff: Mentor

No, you have it right.

10. Jan 6, 2016

### Erland

Perhaps "someone else" meant (2x)2, which has the derivative 8x.