Question

Strange question.. Take the derivative y=(x=2)^8 (x+3)^6

Answer 1

product rule and x^n rule

Answer 2

I wonder if the prof. ended up mistyping. No? really?

Answer 3

wow, I've never seen something like this

Answer 4

is that x=2 inside the brackets ?

Answer 5

i think thats
\(\Large y = (x+2)^8(x+3)^6\)

Answer 6

see, the thing is that it really is an equal sign :/

Answer 7

I think it was a typing error

Answer 8

its definitely their typing mistake

Answer 9

good haha XD

Answer 10

now can you solve it ?

Answer 11

chain rule?

Answer 12

product rule + chain rule + x^n rule

Answer 13

hmm

Answer 14

ok so

Answer 15

if you know those, this is really simple :)

Answer 16

ok so for this one we definitely need the chain rule and the product rule like hartnn stated.

Answer 17

1st step is

Answer 18

\(\Large (fg)' - f'g +fg'\)

here f = (x+2)^8
g = (x+3)^6

Answer 19

\(\Large (fg)' = f'g +fg'\)

Answer 20

8(x+2)^7 (x+3)^6 + (x+2)^8 6(x+3)^5

Answer 21

yes! :)

Answer 22

this?

Answer 23

ok cool

Answer 24

well the product rule says to take the derivative of one part and times it by the other part and then add that to the derivative of the other part times the first part.

Answer 25

now factor out terms, whichever you can

Answer 26

well the (x+2) and (x+3)s

Answer 27

and 2

Answer 28

ah yes

Answer 29

yessss xD

Answer 30

Use logarithms. It becomes much easier. :D

Answer 31

lol no u

Answer 32

only if you love logs :P

Answer 33

hmm so then it is

Answer 34

not for taking the derivative

Answer 35

logs can be used here, but prolly not the best method..

Answer 36

Oh, okay. :)

Answer 37

yeahhh

Answer 38

2(x+2)(x+3)(7)?

Answer 39

O.o

Answer 40

hmm, I've forgotten what happens when you factor out, does it yield an x or a 1?

Answer 41

what is common from
(x+2)^7 and (x+2)^8
?

Answer 42

the (x+2)?

Answer 43

only x+2
?

Answer 44

\(\Large ☺^3 + ☺^5 = ☺^3 + ☺^3 ☺^2 =☺^3(1+☺^2) \)
does that makes sense ?

Answer 45

wait a moment

Answer 46

(x+2)^15 would combine them

Answer 47

why would u combine them ?

Answer 48

ok, I guess it doesn't make sense, I am just remembering these rules with powers

Answer 49

yes, it makes total sense

Answer 50

\(\Large (x+2)^7 + (x+2)^8 = (x+2)^7(1+(x+2))\)
sure ?

Answer 51

in same way, what is common from
(x+3)^6 and (x+3)^5
?

Answer 52

((x+3)^5)(1+(x+3))

Answer 53

correct
so,
8(x+2)^7 (x+3)^6 + (x+2)^8 6(x+3)^5

=...?

Answer 54

hmm

Answer 55

ok writing down

Answer 56

so, it's (2)(x+2)^7(x+3)^5 ((4x+12)+(3x+6))

Answer 57

good!

Answer 58

=(2)(x+2)^7(x+3)^5 (7x+18)

Answer 59

you are \(\huge \color{red}{\checkmark}\)

Answer 60

^_^ is that good enough of an answer. I don't have to simplify this one they say

Answer 61

thats the most simplified form :)

Answer 62

woohoo! :) I appreciate the help

Answer 63

welcome ^_^