Question

Find the derivative of F(x)=3x^2 algebraically using the definition of the derivative.

Answer 1

F(x)=3x^2

F(x) = 3(2)x^(2-1)

F(x) = 6x^1

F(x) = 6x

Answer 2

that is all that it is asking for when it said algebratically it confussed me

Answer 3

are you currently in a section where you have to prove it using limits, epsilon proofs?

the way i solved it above is how you normally solve it.

Answer 4

we are put we just got done learning it the way that you just did it

Answer 5

f ' = lim (h->0) ( f(x+h) - f(x) )/h

Answer 6

I am so confussed

Answer 7

Is the way that you did it algebrtically

Answer 8

no, it is using the definition of the derivative.
first, if given f(x) = 3x^2 then f(x+h) = ....

Answer 9

right I need the algebratically using the definition of the derivative.

Answer 10

got it ?

Answer 11

I got f(3x^2+h)

Answer 12

nope.
if given f(x) = 3x^2 then f(x+h) = 3(x+h)^2
u need expand it :
f(x+h) = 3(x+h)^2 = 3(x^2+2xh + h^2) = 3x^2 + 6xh + 3h^2

Answer 13

ok

Answer 14

now, apply of them to defined of derivative using limit above
f '(x) = lim (h->0) ( f(x+h) - f(x) )/h
= lim (h->0) (3x^2 + 6xh + 3h^2 - 3x^2 )/h
= lim (h->0) (6xh+3h^2 )/h

so far so good ?

Answer 15

yes

Answer 16

now, can u simplify that if all thing in numerator divided by h

Answer 17

yes but you can;t simplify it anmore can you

Answer 18

so wouldn't tht be the answer

Answer 19

= lim (h->0) (6xh+3h^2 )/h
= lim (h->0) 6xh/h + 3h^2/h
= lim (h->0) 6x + 3h

Answer 20

ok got it and that is the answer correct.

Answer 21

just subtitute h=0, u got the answer right :)

Answer 22

you mean so the answer is 6x+3(0)

Answer 23

so then the answer is just 6x

Answer 24

yup

Answer 25

ok thanks

Answer 26

that is how to get derivative by using definition, it is always using limit
you're welcome

Answer 27

thanks

Answer 28

yw again :)