anonymous
  • anonymous
Find the derivative with respect to x of the integral from 2 to x cubed of the natural log of x squared, dx.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
https://gyazo.com/d467d76cdbb0a105dfd1d1d0c7ea8024
anonymous
  • anonymous
it is no wonder that mathematicians invented notation use the equation tool below
anonymous
  • anonymous
I got \[3x^2[\ln(x^2)]\]

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anonymous
  • anonymous
Will wolfram be able to confirm this for me?
anonymous
  • anonymous
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
anonymous
  • anonymous
*two
anonymous
  • anonymous
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
some.random.cool.kid
  • some.random.cool.kid
wolfram is a great site for graphing however take @satellite73 advice instead because wolfram will not cover this. Plus I just tested it...
anonymous
  • anonymous
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
anonymous
  • anonymous
It is
anonymous
  • anonymous
And I just saw my mistake.
anonymous
  • anonymous
wolfram will not be able to do it because it is nonsense
anonymous
  • anonymous
As soon as you posted that equation
some.random.cool.kid
  • some.random.cool.kid
give or take wolfram works 50% of the time for me but it will not help with this stuff i know that much.
anonymous
  • anonymous
I got this \[3x^2[\ln(x^6)]\]
anonymous
  • anonymous
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 \(x^3 \)
anonymous
  • anonymous
^^ I did
anonymous
  • anonymous
yes, that is right, although i would have written \[18x^2\ln(x)\]
some.random.cool.kid
  • some.random.cool.kid
question? why 18? now im confused?
anonymous
  • anonymous
Weird enough wolfram was able to do it originally but when I entered t instead of x it gave me nothing
anonymous
  • anonymous
@Ephemera will explain that to you
anonymous
  • anonymous
https://www.wolframalpha.com/input/?i=d%2Fdx+integral+2+to+x%5E3+ln%28x%5E2%29
anonymous
  • anonymous
Oh it is 18 due to the properties of logarithmic functions
some.random.cool.kid
  • some.random.cool.kid
ah makes sense.
anonymous
  • anonymous
:)

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