Question

Find the derivative with respect to x of the integral from 2 to x cubed of the natural log of x squared, dx.

Answer 1

https://gyazo.com/d467d76cdbb0a105dfd1d1d0c7ea8024

Answer 2

it is no wonder that mathematicians invented notation
use the equation tool below

Answer 3

I got \[3x^2[\ln(x^2)]\]

Answer 4

Will wolfram be able to confirm this for me?

Answer 5

that question is in serious error
where did it i come from? the variable \(x\) is being used in two places to mean to entirely different things

Answer 6

*two

Answer 7

it should read \[\frac{d}{dx}\int _0^{x^3}\ln(t^2)dt\] tell you math teacher this is a big mistake on his/her part

Answer 8

wolfram is a great site for graphing however take @satellite73 advice instead because wolfram will not cover this. Plus I just tested it...

Answer 9

so lets pretend that is what it is and solve it
first off \(\ln(t^2)=2\ln(t)\) by a well known property of the log

Answer 10

It is

Answer 11

And I just saw my mistake.

Answer 12

wolfram will not be able to do it because it is nonsense

Answer 13

As soon as you posted that equation

Answer 14

give or take wolfram works 50% of the time for me but it will not help with this stuff i know that much.

Answer 15

I got this \[3x^2[\ln(x^6)]\]

Answer 16

in any case you need to know two facts: the derivative of the integral is the integrand, and the chain rule
replace \(t\) by \(x^3\) and then multiply by the derivative of \(x^3
\)

Answer 17

^^ I did

Answer 18

yes, that is right, although i would have written \[18x^2\ln(x)\]

Answer 19

question? why 18? now im confused?

Answer 20

Weird enough wolfram was able to do it originally but when I entered t instead of x it gave me nothing

Answer 21

@Ephemera will explain that to you

Answer 22

https://www.wolframalpha.com/input/?i=d%2Fdx+integral+2+to+x%5E3+ln%28x%5E2%29

Answer 23

Oh it is 18 due to the properties of logarithmic functions

Answer 24

ah makes sense.

Answer 25

:)