Question

find the deivative of f(x)=1/x^2

Answer 1

it is -2/x^3

Answer 2

Note that 1/x^2 = x^(-2).

Answer 3

derivative*

Answer 4

this means
\[f'(x)=-\frac{2}{x^3}\]

Answer 5

Hey satellite how can I enter LaTeX in here?

Answer 6

how did you get there?

Answer 7

Using the rule for differentiating polynomials.

Answer 8

d/dx ( x^n ) = n*x^(n-1)

Answer 9

This holds for all real n.

Answer 10

i have to use f(x + dx) - f(x)/dx

Answer 11

Don't forget your parenthesis in the numerator!

Answer 12

yes all of it is in the numerator

Answer 13

you enter latex via
"\[" to open and
"\]" to close

Answer 14

Then you need to use the binomial theorem to prove the identity for general polynomials.

Answer 15

dang didn't work
@Ymanifold come to chat and i can show you there

Answer 16

I get the idea satellite

Answer 17

we haven't learn that

Answer 18

\[ f(x) \]

Answer 19

there you go and if you right click you can see the source

Answer 20

ahhhhhh frustration!

Answer 21

\[\int_0^{\infty}e^{-x^2}dx\]

Answer 22

thanks satellite

Answer 23

welcome
@amber do you have to find this derivative from scratch? using the definition?

Answer 24

yea thats what she has to do

Answer 25

be good practice for your latex. you gonna write it out?

Answer 26

okay i was with you until the end

Answer 27

That is the geometric sum

Answer 28

You need it to expand 1/x

Answer 29

ahhh just forget it ill ask my teacher but thanks for trying!

Answer 30

all i am doing is finding the slope of the tangent curve

Answer 31

What I'm saying is: Use \[ \frac{1}{1-x}=\sum^\infty_{k=0} x^k \]

Answer 32

\[\frac{f(x+h)-f(x)}{h}=\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}\]
\[=\frac{x^2-(x+h)^2}{x^2(x+h)^2h}\]
\[=\frac{x^2-(x^2+2xh+h^2)}{x^2(x+h)^2h}\]
\[=\frac{-2xh+h^2}{x^2(x+h)^2h}\]
\[=\frac{h(-2x+h)}{x^2(x+h)^2h}\]
\[=\frac{-2x+h}{x^2(x+h)^2}\] now you no longer have and h as a factor in the denominator, so take the limit by replacing h by zero and get the answer

Answer 33

Thats much easier :D.

Answer 34

well it is just a bunch of ugly algebra, the gimmick of which is to get the h to cancel top and bottom so you can take the limit

Answer 35

ok i kinda got that! but i had (-2xh - h^2)/x^2(x+h)^2

Answer 36

NEVERMIND!!!
i had that the whole time just was mixed up
THANKS! ((:

Answer 37

lol!

Answer 38

maybe you forgot the h in the denominator, or didn't factor and cancel. good job though

Answer 39

yea i did forget the h