Question

Find the derivative of the function using the definition of derivative.

Answer 1

f(x)= 3+x/1-3x

Answer 2

@phi

Answer 3

how far did you get ?

Answer 4

I cross multiplied the top @phi

Answer 5

3+(x+h)/1-3(x+h) - 3+x/1-3x
-------------------------
h

Answer 6

ignoring the divide by h for the moment,

you have two fractions. Put them over a common denominator
of (1-3x-3h)(1-3x)

Answer 7

that means multiply the first fraction by (1-3x)/(1-3x)

and multiply the second fraction by (1-3x-3h)/(1-3x-3h)

Answer 8

wait let me get in the same pic as you

Answer 9

before I do that step, do I simplify the parentheses ?

Answer 10

for ex: 1-3(x+h)?

Answer 11

you could distribute everything, and get lots of terms (of which most will cancel)

or in the first fraction you can write (3+(x+h)) as (3+x) + h
multiply it by (1-3x) to get (3+x)(1-3x) + h(1-3x)

do the same for the second fraction, write 1-3(x+h) as (1-3x) - 3h

-(3+x)( (1-3x) - 3h )= -(3+x)(1-3x) + 3h(3+x)

Answer 12

the top will be
(3+x)(1-3x) + h(1-3x) -(3+x)(1-3x) + 3h(3+x)

notice that (3+x)(1-3x) - (3+x)(1-3x) = 0

so you get
h(1-3x)+ 3h(3+x)

now distribute the h (and 3h) to get
h -3hx +9h +3hx
which simplifies

Answer 13

Took me a while to process all that. All right, i got it!

Answer 14

so its going to be h-3hx+9h+3hx/ (1-3x)-3h

Answer 15

@phi

Answer 16

or is the answer just 9?

Answer 17

It's 9.