FIrst derivative question

Question

amtran_bus · Answer

Using Newton's definition of the first derivative:
Show that for f(x)=2x^2+2x, f'(x)=4x+2
Prove that for a constant f(x)=c, f'(x)=0

amtran_bus · Answer

I am very new to this, but I understand both answers.  I just need to see how (the formula and why) to get there.

stamp · Answer

Newton's definition of a first derivative? What is that? $$limx->0(f(x+h)-f(x))/h?$$

amtran_bus · Answer

I do have that formula, thanks.
I know that for part one you simply move the exponent out front, making it 4x+2x, however, anytime you have a number and a variable, it is just that number.

I also know that anytime you have a constant, it will "fall" to zero.

I guess I just need the steps so I can see it.

stamp · Answer

I cannot help you until I know what you are talking about, I have honestly never heard of "Newton's definition of the first derivative". I know of other ways of solving derivatives, so if you could explain to me Newton's definition we can try and solve this problem together.

amtran_bus · Answer

Well, the formula you typed is the same I have.  Can you walk me through the steps to prove that     f(x)=2x^2+2x, f'(x)=4x+2  and     f(x)=c, f'(x)=0?   Thanks.

stamp · Answer

Find f(x+h)

amtran_bus · Answer

As in 2*2   =4x?

stamp · Answer

No, as in$$f(x)=2x^2+2$$$$Find\ f(x+h).$$

amtran_bus · Answer

i am stuck

stamp · Answer

If$$f(x)=2x^2+2$$then$$f(x+h)=2(x+h)^2+2$$I want you to simplify f(x+h) for me and let me know what you get.

stamp · Answer

@AmTran_Bus  Are you ok?

amtran_bus · Answer

Yes, thanks.  To be honest, I have never seen X+h or this 1st D stuff ever before.  But I saw the power rule and it made perfect sense for the whole problem. @stamp

stamp · Answer

Yes the power-rule is a good way to find these derivatives, but we need the limit definition of it.

Did you find your f(x+h)?

amtran_bus · Answer

To be honest, I'm not sure how.