Question

f(x)=2x^4x
Logarithmic Derivatives

Answer 1

@jim_thompson5910

Answer 2

4 is the exponent? or 4x is?

Answer 3

4x,
2^(4x)

Answer 4

ok thx

Answer 5

it says f(3)'

Answer 6

y = 2x^(4x)

ln(y) = ln( 2x^(4x) )

ln(y) = 4x*ln( 2x )

derive both sides with respect to x, then solve for y'

Answer 7

1/y?

Answer 8

the derivative of ln(y) with respect to x is ( y' )/y

Answer 9

I see. is this for left hand?

Answer 10

yes

Answer 11

ok,

Answer 12

what do i do for right hand?

Answer 13

use the product rule

Answer 14

4x(1/2x)+(in2x)(4)?

Answer 15

ln is lower case L, then n

not i then n

Answer 16

oh wait, made a typo, hold on while I fix it

Answer 17

y = 2x^(4x)

ln(y) = ln( 2x^(4x) )

ln(y) = ln( 2) + ln( x^(4x) )

ln(y) = ln( x^(4x) ) + ln( 2)

ln(y) = 4x*ln( x ) + ln( 2)

( y' )/y = 4*ln( x )+(4x/2x)*2

( y' )/y = 4*ln( x )+4

y' = y ( 4*ln( x )+4 )

y' = 2x^(4x) * ( 4*ln( x )+4 )

I'll let you finish

Answer 18

sure,

Answer 19

mm product rule?

Answer 20

so

f ' (x) = 2x^(4x) * ( 4*ln( x )+4 )

and you plug in x = 3 to find f ' (3)

Answer 21

yes

Answer 22

It says incorrect again

Answer 23

what did you get

Answer 24

i got 20777773655.1287321453297664

Answer 25

way too big lol

Answer 26

hahaha

Answer 27

although, the answer is quite large...

Answer 28

y = 2x^(4x)

ln(y) = ln( 2x^(4x) )

ln(y) = ln( 2) + ln( x^(4x) )

ln(y) = ln( x^(4x) ) + ln( 2)

ln(y) = 4x*ln( x ) + ln( 2)

( y' )/y = 4*ln( x )+(4x/2x)*2

( y' )/y = 4*ln( x )+4

y' = y ( 4*ln( x )+4 )

y' = 2x^(4x) * ( 4*ln( x )+4 )

f ' (x) = 2x^(4x) * ( 4*ln( x )+4 )

f ' (3) = 2(3)^(4(3)) * ( 4*ln( 3 )+4 )

f ' (3) = 8,922,308.90641656

Answer 29

of course, you'll leave off the commas

they're just there for display purposes

Answer 30

2.0777?

Answer 31

how did you get that?

Answer 32

by my cauclator,

Answer 33

it says 2.077777366e10

Answer 34

oh, that's close I guess, but what I got should be the correct answer

Answer 35

what is ur answer?

Answer 36

i posted it above

Answer 37

see it?

Answer 38

yes, omg,
you are math talent

Answer 39

no, that would be the calculator lol

Answer 40

i wish i could calculate that in my head

Answer 41

thank you, the way you write is clear to see,
easy to learn

Answer 42

yw

Answer 43

can i post more questions?

Answer 44

sure