Question

I want to determine the first derivatives.
y=(x+2)^2(2x-1)^3

Answer 1

the solution step by step

Answer 2

YOu dont need to use the definition of a derivative do you?

Answer 3

I cannot understand all of above at all. Do you have any easier method than this.

Answer 4

this is how I do derivatives,

y=(x+2)^2(2x-1)^3

Split it into smaller functions,

g(x) = (x+2)^2
m(x) =(2x-1)^3

We can split these new functions into even simpler functions so lets do that

Starting with g(x)

d(x) = x^2
s(x) = x+2

now take the derivative of these two smaller functions,

d(x) = x^2
d'(x) = 2x

s(x) = x + 2
s'(x) = 1

Now we notice that this is one function in another function so we can just apply chain rule which is,

g'(x) = d'(s(x))*s'(x)

sub in,

g(x) = (x+2)^2
g'(x) = 2(x+2)*1

Now do the same with m(x)

you should notice right away that you have to use product rule with g(x) and m(x) so just use the product rule formula which is,

f'(x) = g'(x)m(x) + g(x)m'(x)

Answer 5

Follow my method

Answer 6

it is the best way to take a derivative you will never make a mistake and you will train your brain to be able to solve them in your head

Answer 7

if you have any questions please ask, I can complete the problem if you are confused

Answer 8

I can walk you through m(x) and the final derivative if you like but I would prefer that you tried my method first

Answer 9

try deriving m(x) then the final derivative, I have no idea why this isn't taught in most schools

Answer 10

wahh, thanks a lot Australopithecus but... I have a problem with complete this using f'(x) = g'(x)m(x) + g(x)m'(x)

Nt very expert. I find it little hard

Answer 11

you understand function notation right?

that g(x) is just another way of writing (x+2)^2 it is just faster

Answer 12

Can you show me what you got for the derivative of m(x)? Just do it exactly as how I did the derivative of g(x)

If you dont have the basic rules of derivatives down then I recommend having them in front of you

Answer 13

Once you get this method down you only really need to memorize chain rule, product rule and maybe quaint rule depending on if your prof cares

Answer 14

for
m(x) = (2x-1)^3
m'(x) = 6(2x-1)^2

correct?

Answer 15

looks good to me

Answer 16

now just sub into the product rule equation

Answer 17

g(x) and m(x) its that easy

Answer 18

BTW since I showed you chain rule and product rule.

I might as well show you quotient rule which is:

f(x) = g(x)/s(x)
f'(x) = [g'(x)s(x) - s'(x)g(x)]/(s(x))^2

Answer 19

those are the three formulas you have to memorize

Answer 20

practice using my method and this stuff will be a joke to you

Answer 21

ok, i will .
Here what I got this after subs it,
2(x+2)(2x-1)^3 + (x+2)^2 (6(2x-1))^2

But i dont know how to complete this. can you show please...

Answer 22

tbh though quotient rule is useless it is just derived from product rule, simply use the rule:

\[x^{-1} = \frac{1}{x}\]

and you can use product rule always, for example

f(x) = s(x)/d(x)
f(x) = s(x)d(x)^-1

f'(x) = s'(x)d(x) + s(x)d'(x)^-1

Answer 23

2(x+2)(2x-1)^3 + (x+2)^2 (6(2x-1))^2

This is wrong, look at it and you will see why right away

Answer 24

its not that you didnt apply the method correctly

Answer 25

you made an algebraic mistake

Answer 26

which one, i cant see it

Answer 27

2(x+2)(2x-1)^3 + (x+2)^2 (6(2x-1))^2
/\

Answer 28

see it now?

Answer 29

you squared the 6

Answer 30

(6(2x-1))^2 = 6^2(2x-1))^2 =/= 6(2x-1)^2

Answer 31

(6(2x-1))^2 = 6^2(2x-1))^2 =/= 6(2x-1)^2 = m'(x)

Answer 32

show me the answer :D

Answer 33

careful when subbing into the formulas

Answer 34

2(x+2)(2x-1)^3 + (x+2)^2 (6(2x-1)^2) like this?

Answer 35

then help me how to complete this

Answer 36

I would just expand out the polynomial and then take the derivative.

Answer 37

you cant avoid chain rule

Answer 38

that is the answer

Answer 39

but not the final answer... how must I do it?

Answer 40

f'(x) = g'(x)m(x) + g(x)m'(x)

m(x) = (2x-1)^3
m'(x) = 6(2x-1)^2

g(x) = (x+2)^2
g'(x) = 2(x+2)*1

f'(x) = 2(x+2)(2x-1)^3 + 6(2x-1)^2((x+2)^2)

Answer 41

that is the final answer

Answer 42

they might want you to simplify it

Answer 43

but that is the derivative

Answer 44

yup, tht right

Answer 45

be very very careful how you set up your brakets

Answer 46

you would have been right but you placed your brackets incorrectly and squared the 6 in m'(x)

Answer 47

the final answr suppose to be: 10(2x-1)^2(x+2)(x+1) how is it done? show me

Answer 48

@wio

that is awful advice what if she was asked to take the derivative of f(x) = (3 + x)^99

You can't avoid chain rule in calculus

Answer 49

just simplify

Answer 50

Your first question?\[\Large \color{royalblue}{\text{Welcome to OpenStudy Sytee! :)}}\]

Answer 51

@zepdrix yup, thanks :')

Answer 52

don know how to simplify it

Answer 53

what's up @zepdrix

Answer 54

f'(x) = 2(x+2)(2x-1)^3 + 6(2x-1)^2((x+2)^2)

collect like terms first off

f'(x) = (x+2)(2x-1)^2[2(2x-1) + 6(x+2)]

Answer 55

can you do the next step? I'm simply using the rule

a(x + b) = ax + ab

Answer 56

in the last step

Answer 57

you are almost to where you want to be with,

f'(x) = (x+2)(2x-1)^2[2(2x-1) + 6(x+2)]

Just fool around with, 2(2x-1) + 6(x+2)

Answer 58

You seriously need to have algebra mastered if you are going to be successful in calculus.

I recommend looking up math rules and committing them to memory if you have any doubts about what you can and cannot do mess around with,
www.wolframalpha.com

to convince yourself of the basic math rules

Answer 59

ok, i get it now. thankyou

Answer 60

ok awesome :D

if you have any other questions feel free to message me take care and good luck

Answer 61

i have a lot of question to ask you actually

Answer 62

oh really

Answer 63

well Im going to sleep soon so if you have them ask them

Answer 64

um, if you don mind, show me the next step plz

Answer 65

can you at least expand them
2(2x-1) + 6(x+2)

Answer 66

(4x-2)+(6x+12)

Answer 67

if you give me all the solution step, maybe I can revise it and look bck what I really didnt understand it.

Answer 68

you can remove the brakets

Answer 69

I shouldnt have to its pretty much solved

Answer 70

you can do this algebra I believe in you!

Answer 71

Add/subtract like terms and use

a(x+b) = ax + ab

and you are done

Answer 72

ok, i will try now..

Answer 73

ooops

Answer 74

sorry it should be

4x-2 + 6x+12

so you have,

(x+2)(2x-1)^2[4x-2 + 6x+12]

and you want

10(2x-1)^2(x+2)(x+1)

Answer 75

do you have it solved?

Answer 76

not yet, still confusing me.
this one, (x+2)(2x-1)^2 must I multiple each of them

Answer 77

no they are in your final answer leave them alone

Answer 78

you only care about [4x-2 + 6x+12]

Answer 79

or you should only care about simplifying that

Answer 80

omg, i solve it!

Answer 81

good job

Answer 82

thanks a lot!!!

Answer 83

my pleasure

Answer 84

you may go to ur beauty sleep now. :)

Answer 85

Ok good to hear you are done with me, good luck with calc