Question

derivative of f(x)=x^2+4x+5

Answer 1

Are you wanting the formal definition of derivative to be applied or just short cuts?

Answer 2

either one will be fine :)

Answer 3

Well how about we use the formal definition of derivative because applying the short cuts is terribly easy here.

Answer 4

So do you know the formal definition of the derivative?

Answer 5

yes

Answer 6

\[f'(x)=\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h} \\ f'(x)=\lim_{z \rightarrow x}\frac{f(z)-f(x)}{z-x}\]
which way do you like
the first one or the second one

Answer 7

first

Answer 8

Well we already have f(x) is x^2+4x+5
and f(x+h) is?

Answer 9

i honestly forgot how to do this :X

Answer 10

would it be just 2x+4 since 5 would be 0

Answer 11

\[f(x)=x^2+4x+5 \\ f(fish)=(fish)^2+4(fish)+5 \\ f(x+h)=(x+h)^2+4(x+h)+5\]

Answer 12

\[f'(x)=\lim_{x \rightarrow h}\frac{(x+h)^2+4(x+h)+5-(x^2+4x+5)}{h}\]

Answer 13

now my advice to you is multiply the top out fully
then combine any like terms on top

Answer 14

how is it going so far?