Can I Use the Power Rule to Get the Derivative Here?

[Danatron]

can i use the power rule to get the derivative here?

f ' (x) = 3x^2 - 2(2x^1) + 1

 

[adjacent]

Of course, why not? Do you use any other rule for that?
Your answer is correct

 

[Danatron]

ok good, so i wouldn't go again until there were no powers?

eg. f ' (x) = 2(3x) - 2(2x) + 1

 

[adjacent]

ok good, so i wouldn't go again until there were no powers?

eg. f ' (x) = 2(3x) - 2(2x) + 1

No. Why do you have to differentiate it again? The notation $f'(x)$ means-Differentiate once. Similarly, the notation $f''(x)$ means differentiate twice.

In leibniz notations $\frac{\text{d}}{\text{d}x}$ means- Differentiate once and $\frac{\text{d}^2}{\text{d}x^2}$ means- differentiate twice and so on.

In your example,(differentiating twice) you should write $f''(x)$ and this should be equal to the derivative of $3x^2 - 4x + 1$ which is $6x+4$
Note that the derivative of a constant (1) is zero.

So in general, we differentiate the function $f$, and again differentiate the derivative of the function $f$, to differentiate $f$ twice. This can also be extended to differentiating 10000 times