Question

Could I get an explanation of the power rule on derivatives? ..
For example;
4x^3 - 5x^1/3 +3x^-2

Answer 1

Suppose you have: \(\sf \color{red}{ax^{n}}\), if youre trying to find the derivative: \(\sf \color{}{\frac{d}{dx}(ax^n) = nax^{n-1}}\)

Answer 2

Oh, so
I know 4x^3 becomes 12x^2

Answer 3

So for the first one, you have 4x\(^3\), it would be: \(\sf \color{blue}{3 \times 4x^{3-1}}\)

Answer 4

Yeah, 12x\(^2\)

Answer 5

What would -5x^1/3 and 3x^-2 become?..

Answer 6

\(\sf \color{red}{\frac{1}{3}(5)x^{\frac{1}{3}-1}}\)

Answer 7

ah,
so
5/3 x^ -2/3 ?..

Answer 8

But you can't have a negative exponent..

Answer 9

Why not?

Answer 10

Aren't you suppose to put something like x^-2 into 1/x^2

Answer 11

or do i just leave it as that?.

Answer 12

\(\sf \color{}{x^{-\frac{2}{3}}=\frac{1}{x^{\frac{2}{3}}}}\) or \(\frac{ 1 }{ \sqrt[3]{x^2} }\)

Answer 13

Alright, so would
3x^-2
become
-6/x ?

Answer 14

No. -2-1 = -1?

Answer 15

so just -6x^-1 then..

Answer 16

\(\huge -2-1 = -1?\) really??

Answer 17

oh oops, -3 LOL

Answer 18

still morning forgive me .. >.>

Answer 19

You're such a noob. I'm done with you. Good bye.

Answer 20

LOL

Answer 21

alright thanks :P