Question

Find the indicated derivative and simplify:

y' if y=[ln(x^2 + 3)]^3/2

Answer 1

use ln on both sides

Answer 2

y' = (3/2)[ [ln(x^2 + 3)]^1/2 ]* [2x/(x^2 + 3)]
y' = [3x/(x^2 + 3)] * [ln(x^2 + 3)]^1/2 ]

Answer 3

id just use chain rule, but i love the chain rule

Answer 4

attempting the chain rule but not sure if I am doing it correctly.

Answer 5

look at what i did .. i used the chain rule

Answer 6

i think you missed a derivative there coolsector, you forgot the derivative of lnx

Answer 7

nvm

Answer 8

saw you had just simplified it :D

Answer 9

no i havent .. "[2x/(x^2 + 3)]" this is the derivative of the ln

Answer 10

@Fakshon
is this ok for you ? y' = [3x/(x^2 + 3)] * [ln(x^2 + 3)]^1/2 ]

Answer 11

It can't be simplified any further can it?

Answer 12

cant

Answer 13

I got the same thing, but figured I did something wrong because I thought it had to be done differently.

Answer 14

no.. its fine

Answer 15

OK great thanks so much. At least I feel vindicated, lol.

Answer 16

:)

Answer 17

(3/2)(ln(x^2+3))^(1/2)(1/(x^2+3))(2x))

Answer 18

Ohh someone else posted. Okay then :P .

Answer 19

its ok .. another verification

Answer 20

yea thanks

Answer 21

I guess if you wanted to simplify further you could use the laws of logarithms but I think that pretty simplified.

Answer 22

(3/2)(ln(x^2+3))^(1/2)(1/(x^2+3))(2x))