Question

help please :)

Answer 1

Find the derivative of f(x) = 8x2 + 11x at x = 7.

Answer 2

hello :)

Answer 3

first, find f`(x)

Answer 4

can you just take the derivative of the function term by term?

Answer 5

go ahead, don't be afraid to interrupt me

Answer 6

i am sorry but i dont really understand this :/

Answer 7

can instead of using this question like make one up and just show me how to do it :)

Answer 8

i learn better by seeing than being walked through xD

Answer 9

you need to find the derivative, and to then plug in 7 for x into the derivative.
I can give you a different example, sure:)

here....

Answer 10

thank you xD

Answer 11

Find the derivative of \(f(x)=3x^3-2x^2+x+2\) at x = 2.
---------------------------------------------------

Steps:
1) Find the derivative of the function.
2) Plug in 2 for x into the derivative.

Solutions:

\(\large\color{black}{ \displaystyle f(x)=3x^3-2x^2+x+2 }\)
(taking the derivative. BELOW)
\(\large\color{black}{ \displaystyle f'(x)=\color{red}{3\times }3x^{\color{red}{3}-1}-\color{red}{2\times }2x^{\color{red}{2}-1}+\color{red}{1\times }x^{\color{red}{1}-1}+0 }\)
(I demonstrated how power rule works here, just in case)
\(\large\color{black}{ \displaystyle f'(x)=9x^2-2x^2+1+0 }\)
simplifying,
\(\large\color{black}{ \displaystyle f'(x)=9x^2-2x^2+1 }\)

now, you need the derivative at x=2,
\(\large\color{black}{ \displaystyle f'(2)=9(2)^2-2(2)^2+1 }\)
\(\large\color{black}{ \displaystyle f'(2)=36-8+1 }\)
\(\large\color{black}{ \displaystyle f'(2)=29 }\)

Answer 12

back :)

Answer 13

k, after you read my short example, say if you have any questions. Ask absolutely anything you are not comfortable with.

Answer 14

what is the power rule? if i heard this so many times from other people but i still don know what it is :/

Answer 15

oh, ok

Answer 16

i did here someone say there where more than one

Answer 17

\(\large\color{royalblue}{ \displaystyle \frac{d}{dx}~\left[~x^{\rm n}~\right]={\rm n}\cdot x^{{\rm n}-1}}\)

d/dx is the notation for a derivative of a function with respect to x (i.e. that x is the input/independent variable).

n is just some number (for any \(\rm n\) asides from n=0)

Answer 18

and then there is another rule, that involves having x to some power multiplied by a constant (i.e. w/ a coefficient in front)

Answer 19

it goes as follows

Answer 20

so how would i use this fro the problem?

Answer 21

\(\large\color{royalblue}{ \displaystyle \frac{d}{dx}~\left[~{\rm a} \cdot x^{\rm n}~\right]={\rm a} \cdot{\rm n}\cdot x^{{\rm n}-1}}\)

Answer 22

I will show you how I did it for my example, because you apparently didn't understand it fully. we will go through it together.

Answer 23

thank you :)

Answer 24

the derivative of \(x^n\) is \(n \times x^{n-1}\)

so, if I wanted to find the derivative of \(x^2\) what would my derivative be?

Answer 25

1?

Answer 26

\(x^2\) will have a derivative of \(2\times x^{2-1}\) which simplifies to \(2x\)

Answer 27

you multiply times the power, and then decrease the power by 1.

Answer 28

ohhhh k i see

Answer 29

k, tell me what is the derivative of \(x^3\) ?

Answer 30

it would be 3x3x^2

Answer 31

making it 9x^2

Answer 32

why?

Answer 33

ohhhh my bad i miss red lol

Answer 34

\(x^3\) will have a derivative of \(3\times x^{3-1}\)

Answer 35

3x^2

Answer 36

i for somereason read a 3 innfront of x lol

Answer 37

oh... ok, a different one

ok, how about derivative of \(x^4\) ?

Answer 38

4x^3

Answer 39

yup

Answer 40

and derivative of \(2x^3\) ?

Answer 41

then for my first question which is 8x^2 would i get 16x?

Answer 42

yes

Answer 43

and 11x ?

Answer 44

thank you xDDDD

Answer 45

yw, and 11x will have a derivative of?

Answer 46

11x stays 11 corret

Answer 47

1

Answer 48

because the power 1

Answer 49

1x11x

Answer 50

then if we minus it turns into the power of 0 o.o

Answer 51

\(11x\) is same as \(11x^1\) and has a derivative of \(1\times 11x^{1-1}\) which is: 11

Answer 52

this way any \({\rm C}x\) will have a derivative of just C.

Answer 53

clear?

Answer 54

yea :)

Answer 55

ok, and I know we have no constants in the function, but can you tell me what is the derivative of a constant.

for example, what is the derivative of 7?

Answer 56

their would be no derivative

Answer 57

correct...?

Answer 58

derivative of the function is the slope of the function, correct?

Answer 59

ok

Answer 60

what is the slope of the line y=C ?

Answer 61

since it is rise over run it would be 0/1?

Answer 62

the line never rises nor falls

Answer 63

just stays constant

Answer 64

yes, when you choose any 2 points (a,c) and (b,c) on a horizontal line y=c you get

\(\large\color{royalblue}{ \displaystyle m=\frac{c-c}{a-b}=0}\)

(that is a general prove for the slope of a horiz. line)

Answer 65

and that is why we have a rule that the derivative of a constant is 0.

Answer 66

ohhhhhh

Answer 67

the derivative of a constant (that is the slope of the function y=C, where C is a constant), is 0.

Answer 68

so if i had a funtion like 4x+8 at x=4
then i would get fx=4+0

Answer 69

if you have a function f(x)=4x+8
then your derivative would be

f`(x)=4+0
f`(x)=4

no mater what you plug in for x, you get 4 for f`(x), THAT MEANS that at any point x=a, the slope of the function is 4. Which is true because it is a straight line and its slope doesn't change.

Answer 70

ok thank you so much :)

Answer 71

if only i could medal you more than once

Answer 72

ok, so just some things in general I wanted to post for final clarifications. (if you won't understand my notations, please ask, because those will be frequently used).


(rule 1)
\(\large\color{royalblue}{ \displaystyle \frac{d}{dx}~\left[~ x^{\rm n}~\right]={\rm n}\cdot x^{{\rm n}-1}}\)


(rule 2)
\(\large\color{royalblue}{ \displaystyle \frac{d}{dx}~\left[~{\rm a} \cdot x^{\rm n}~\right]={\rm a} \cdot{\rm n}\cdot x^{{\rm n}-1}}\)


(rule 3)
\(\large\color{royalblue}{ \displaystyle \frac{d}{dx}~\left[~{\rm C} ~\right]=0}\)

Answer 73

wait what if its like -7/x ?

Answer 74

(don;t worry about medals, I got 8k or over)

Answer 75

then you would also apply the power rule

Answer 76

and it would be -7?

Answer 77

\(\large\color{royalblue}{ \displaystyle \frac{d}{dx}~\left[~(-7)\cdot x^{-1} ~\right]}\)

Answer 78

^
^
that is what you are finding

Answer 79

becouse i have a question that asks -7/x at x=-3

Answer 80

ok, first, rewrite the function.

f(x)=-7/x is same as f`(x) = (-7) \(\cdot \) x\(^{-1}\)

Answer 81

then apply the power rule

Answer 82

typo in my post when I said `ok, at first`

the very last function is f(x) not f`(x)

Answer 83

the power rule would make it (-7)*0?
and its ok i still understood it :)

Answer 84

my answer choices are:
3/7
9/7
7/3
7/9

Answer 85

I got disconnected, my apologies.

Answer 86

its ok :)