Question

8e^x + 4 lnx^3. Find the derivative.

Answer 1

Let's do it part by part :)

Answer 2

ok! thanks

Answer 3

What's the derivative of 8e^x? :)

Answer 4

8 or just 8e^x ;-/

Answer 5

It's 8e^x because e^x doesn't change :)

Answer 6

Note that the derivative of 8x would be 8 though

Answer 7

would any of the rules apply? like chain rule? no product or quotient because its not multiplication or a fraction, right?

Answer 8

ok, noted.

Answer 9

Not any of the rules that you've learnt would apply to e^x, so you only have to memorize it by heart :)

Answer 10

I meant apply to the original problem?

Answer 11

Well, you can treat it as (8e^x)' = 8(e^x)' = 8e^x Then you'd have applied the "multiplication by constant" rule

Answer 12

I mean \(\Large\frac d{dx}8e^x=8\frac d{dx}e^x=8e^x\)

Answer 13

ok!

Answer 14

what about the other part of the original question?

Answer 15

Should we proceed to the second part?

Answer 16

Oh

Answer 17

Let's proceed to the second part :)

Answer 18

ok :-)

Answer 19

What's the derivative of 4lnx^3?

Answer 20

I'm not positive how to go about finding the derivative for this part

Answer 21

use power rule?

Answer 22

Power rule is not applicable to this problem :)

Answer 23

Don't forget that ln x^n = nlnx

Answer 24

so 3lnx

Answer 25

Don't forget the 4 in front of it :)

Answer 26

multiply? 12lnx... Im probably making stuff up...i tend to create my own math :-(

Answer 27

Yep that's correct, let's now proceed to the derivative :)

Answer 28

yay!

Answer 29

What's the derivative of 12lnx? :)

Answer 30

would it be 12? because derivative of lnx =1?

Answer 31

Derivative of lnx isn't 1 :/

Answer 32

;-(

Answer 33

I'm not sure then

Answer 34

It's 1/x, memorize this :)

Answer 35

so then it would be 12/x?

Answer 36

Exactly :)

Answer 37

Now let's add the result of the first part and the result of the second part together :)

Answer 38

ok

Answer 39

8e^x + 12/x, right or no?

Answer 40

Perfect :D

Answer 41

you are awesome!

Answer 42

Can i trouble for help with two more? if not, no worries. I just have to run home and then hop back on

Answer 43

Sure! :)

Answer 44

Find the derivative ln(ln7x).

Answer 45

Chain rule is the way to go :)

Answer 46

I was thinking chain rule but ln is not a function by itself

Answer 47

ln is a function by itself

Answer 48

omg..i think my teacher may be wrong then.

Answer 49

so u=ln7x
u'= ln(u)

Answer 50

Does the apostrophe mean derivative of?

Answer 51

yes

Answer 52

Then how would u' be equal to ln(u)

Answer 53

y=ln(u) though

Answer 54

the problem says find f'x for f(x)=ln(ln7x)

Answer 55

Okay I mean f(x)=ln(u)

Answer 56

Where u=ln(7x)

Answer 57

Now find f'(x) :)

Answer 58

Ok, I'm thinking f'(x) of ln7x is 7/x, right or wrong?

Answer 59

Wrong

Answer 60

wait, it would be 1/x

Answer 61

1. There's no such thing as f'(x) of ln7x because f(x) is already defined to be ln(ln(7x))

Answer 62

2. Yep it's 1/x

Answer 63

are you a math teacher? :-)

Answer 64

No, I'm Form 3 (grade 9 in US educational system)

Answer 65

I'm probably younger than you lol

Answer 66

no way! so youre like how old?

Answer 67

14 years old :)

Answer 68

lol! i feel like such an idiot now. yowza! i am in pre-calc for college. *puts head down in disgrace*

Answer 69

xD

Answer 70

ok, back to original problem...

Answer 71

Find f'(x) :)

Answer 72

\[\frac d{dx}\ln(\ln(7x))=\frac d{d\ln(7x)}\ln(\ln(7x))\times\frac d{dx}\ln(7x)\]

Answer 73

that looks like a foreign language to me... sigh ok, let me try

Answer 74

the ds cancel out, and youre left with 1/ln(7x)

Answer 75

No the ds don't cancel out

Answer 76

darnit

Answer 77

\(\dfrac d{dx}g(x)\) means \(g'(x)\)

Answer 78

The ds are just notation

Answer 79

oh i see i do remember seeing that

Answer 80

1/ln(7x) and im stuck now

Answer 81

\[[f(g(x)]'=f'(g(x))\times g'(x)\]

Answer 82

u(x)=ln(7x)
v(x)=ln(x)

f(x)=v(u(x)

Answer 83

f'(x) = [v(u(x))]' = v'(u(x)) * u'(x)

Answer 84

so 1/x (ln(7x)) * u'(x).....I know im prolly not getting it :-(

u'(x)=1/x

Answer 85

For example, \(\sin(5x)'=\cos(5x)\times5\)

Answer 86

For example, \(\cos(\sqrt x)'=-\sin(\sqrt x)\times\dfrac1{2\sqrt x}\)

Answer 87

1/ln(7x) * (1/7x)= 1/7xlnx, correct or no?

Answer 88

It's not 1/7x

Answer 89

right you said that, excuse my brain! its 1/ln(7x) * (1/x)= 1/7xlnx

Answer 90

Again, it's not 1/7x

Answer 91

:-/ ok, give me sec

Answer 92

The part to the left of the equal sign is correct

Answer 93

ok, so does it get simplified further or no? 1/ln(7x) * (1/7x), can I leave it as is?

Answer 94

i meant 1/x* sorry

Answer 95

\[\frac1{\ln(7x)}\times\frac1x=?\]

Answer 96

1/ ln (7x) (x), im not sure if i should square x

Answer 97

Perfect

Answer 98

yay! so f'(x) of f(x) =ln(ln7x)= 1/ ln (7x) (x)