Question

Use the definition of a derivative to calculate f'(8) where f(x)=x+3

show steps.

Answer 1

Definition of a derivative\[\frac{ d }{ dx }x ^{n}= nx ^{n-1}\]a number, like 3, is just \[3x ^{0}\]So when the 0 comes out in front the whole thing becomes zero.

Once get f'(X) just plug in 8. For this particular problem however you are going to get f'(8) = 1 which means at all points x the slope is 1

Answer 2

this is actually not the definition of a derivative

the definition is:


lim h -> 0 [ (f(x+h) - f(x))/h ]

Answer 3

I guess "definition" is the wrong word to use, but that is the form

Answer 4

so we have f(x) = x+3 and f(x+h) = (x+h)+3

notice for the f(h+x) we just put in x+h where we saw an x

Answer 5

yes, this is the form for the exponential shortcut rule.

Answer 6

@xkat you with me?

Answer 7

Listen to @zzr0ck3r he is solving this problem the way it is asked in the question. I'm sorry for a possible confusion

Answer 8

yes, i am with you. keep going.

Answer 9

its all good, I thought the same thing @ChmE and googled it real fast to make sure:P

Answer 10

ok so we have

(f(x+h) - f(x))/h = ?

Answer 11

just write it out as you see it, i told you what f(x+h) was and what f(x) was so write f(x+h) then put a subtraction sign, then write f(x) and put all of that over h

Answer 12

so it would be (8+h)+3-(8+3)/h?