functions and derivatives

[amzamz]

When changing a function into a derivative, using the rule Cnxⁿˉ�, I can do the first part and undertstand it, but not the second;

Function; 2x� - 3x� + 2x - 4

Derivative; 6x� + -6x + 2

I can't understand how we get from 2x - 4 to 2, I'm fine with all the beggining parts, just not the ending. Please help.

[eltelioni]

The derivative of 2x is 2 and the derivative of 4 is 0.
If you think of the derivative as the rate of change of the function with respect x then you will see that the 4 does not contribute because it doesn't change as x changes.

[fo3nix]

You can split up a function into individual functions, anywhere with +'s and -'s.

So D[2x� - 3x� + 2x - 4] (which I'll write as meaning the derivative of that function of x), is the same as D[2x�] - D[3x�] + D[2x] - D[4].

You can use the rule you wrote above with these simple functions. You multiply the function by its power (bring the power to the front), then subtrack 1 from the power.

So,

D[2x^3] = 6x^2
D[3x^2] = 6x
D[2x] = 2
D[4] = 0

So the answer = 6x^2 - 6x + 2.

[kempie]

Also, you can consider that

4 = 4x� (since x� or {x to the power zero} = 1)

The derivative then becomes 0 x 4xˉ� which is 0

[factor-fiction]

The only point I can add to these answers is to clarify that 2x is the same as 2x�, and using your formula the derivative of 2x� is 2x� which equals 2 .

[peanut273]

My answer - Just dont do it!!! :)