Question

Can anyone help me with derivatives?

Answer 1

yup.

Answer 2

yeah

Answer 3

what's the question?

Answer 4

Find the formula for the derivative f(x) = c

Answer 5

derivative of the constant is 0.
but do u need to use the defination for this ?

Answer 6

did u just start with this topic ?

Answer 7

if u need to do it with the definition, do u know what the definition is ?

Answer 8

The definition is the difference quotient, right?

Answer 9

like limit h-> 0 (f(x+h)-f(x))/h
is this what u have ?

Answer 10

if thats what u have then f(x)=c
find f(x+h).
can u ?

Answer 11

Do I put in c for x and solve the quotient?

Answer 12

can u tell me what quotient formula you have ?

Answer 13

if u don't have, you can use the limit formula i mentioned.
to find f(x+h) , replace all 'x' in f(x) by 'x+h'
do u see any x in f(x) ?

Answer 14

I have the one you gave me!

Answer 15

great! so could you find f(x+h) ?

Answer 16

And no! I don't see any X.

Answer 17

ok. so there is nothing in f(x) to replace by 'x+h'
so f(x+h) = c
make sense ?

Answer 18

now just put the values in formula
f(x) =c
f(x+h) = c
what do u get ?

Answer 19

I'm not sure...what do you do with 3 variables?

Answer 20

which 3 variables u talking about ?

Answer 21

x, h and c

Answer 22

\(\huge f'(x) = \lim_{x->0} \frac{f(x+h)-f(x)}{h} \\\large =\lim_{x->0} \frac{c-c}{h}\)
what does the numerator get simplified to ?

Answer 23

h?

Answer 24

i was talking about numerator only..
what is c-c = ?

Answer 25

ohh. 0

Answer 26

so u have limit of 0/h
and 0/h=?

Answer 27

0!

Answer 28

So they want me to do the same thing with f(x) = mx + b. I plug in (x + h) for x?

Answer 29

so you have limit x->0 of 0.
limit of constant is constant.
which gives u f'(x)=0
hence derivative of f(x) = c is 0
ok?

Answer 30

yup, just replace 'x' by 'x+h' in f(x)=mx+b

Answer 31

so what do u get f(x+h) as ?

Answer 32

m(x+h) + b

Answer 33

yes thats correct,
now u need to find the difference f(x+h)-f(x) = m(x+h)+b-(mx+b) =?

Answer 34

(mh+b)/h?

Answer 35

doesn't the b get cancelled also ?

Answer 36

OH! Yes it does! So just mh/h, which is m!

Answer 37

that is correct :)
so limit of m is also m
because m is constant,
hence f'(x)=m
get it ?

Answer 38

I think I do! Can I ask you one more to be sure?

Answer 39

ask as many as you want :)

Answer 40

Okay, thank you! You're very helpful :) Next question: f(x) = sin x

Answer 41

have you solved limits question before ?
u know what is lim x->0 sinx/x = ?

Answer 42

0, right?

Answer 43

nopes.
it is 1.
u also will need the formula for sin(A+B)
do u know it ?

Answer 44

cos a x sin b + sen a cos b?

Answer 45

yup. but did u solve limits questions before?
if not, its not right to jump into derivatives.

Answer 46

I have solved limits, and I THINK I understand them, just not very well.

Answer 47

good.
so u have f(x+h) = sin (x+h)
f(x) = sin x
so
f(x+h)-f(x) = sin(x+h)-sin x
use sin (A+B) to expand sin(x+h)
and tell me what u get.

Answer 48

cos(x)sin(h) + sin(x)cos(h) - sin(x)

Answer 49

that is correct :)
now u have h in denominator.
so separate the denominator, and u will have 3 terms
find limits individually
tell me what u get

Answer 50

Do I need to use a calculator to find the individual limits?

Answer 51

u only need the formula: lim x->0 sinx/x =1
and put x=0 in remaining fraction.

Answer 52

1!

Answer 53

the final answer 1 ??
nopes.
did u separate the denominator to get 3 terms, or should i show u that step?

Answer 54

well, cos(x)sin(h)/h is 1
sin(x)cos(h)/h is 0?
and sin(x)/h is 0 as well?

Answer 55

lim h->0 sin h/h = 1
so
lim h->0 cos x (sin h/h) = cos x(1) = cos x
did u understand this ?

Answer 56

Oh. I thought you said put 0 in for x!

Answer 57

But yes, I get it :)

Answer 58

now from other 2 terms u will have (1-cos h)sin x / h
there is standard formula:
lim y->0 (1-cos y)/ y =0
so both of those terms comes out to be 0
so the final answer is just cos x.
did u understand how ?

Answer 59

How is it (1-cos h)sin x/h?

Answer 60

oops, i meant cos h-1
now ok?

Answer 61

I don't understand. Is that all that remains from both of the last two terms?

Answer 62

yes, last 2 terms ---> sin(x)cos(h) - sin(x)
so
sinx (cos h-1)
and there was h in denominator

Answer 63

so what happened to the sinx?

Answer 64

since lim h->0 (cos h -1) / h = 0
so ,sin x(0) = 0

Answer 65

Ohh. Okay, I see.

Answer 66

did u get all the steps ?
and how the final answer comes out to be cos x ?
could u put all steps together ?

Answer 67

I think I understand. And even though I still have more questions for you, it is very late for me and I have to go to bed now :// Can I ask you more questions tomorrow? You're helped me a lot!

Answer 68

sure, u can ask :)
if i am online.

Answer 69

Okay, I hope I can catch you then! Thank you so much!