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Applying Product Rule

  • #1
Hi I am 14 and attempting to learn calculus I have just proved product rule and am beginning examples of how it might work. Could anyone check, I will write my process.
[tex]y(x)=(12x^6)(7x^4+6)=[/tex]
[tex](12x^6)'(7x^4+6)+(12x^6)(7x^4+6)'=[/tex]
[tex](72x^5)(7x^4+6)+(12x^6)(28x^3)=[/tex]
[tex]504x^9+432x^5+336x^9=[/tex]
[tex]y(x)=840x^9+432x^5[/tex]
 

Answers and Replies

  • #2
1,039
2
Hi I am 14 and attempting to learn calculus I have just proved product rule and am beginning examples of how it might work. Could anyone check, I will write my process.
[tex]y(x)=(12x^6)(7x^4+6)=[/tex]
[tex](12x^6)'(7x^4+6)+(12x^6)(7x^4+6)'=[/tex]
[tex](72x^5)(7x^4+6)+(12x^6)(28x^3)=[/tex]
[tex]504x^9+432x^5+336x^9=[/tex]
[tex]y(x)=840x^9+432x^5[/tex]
Let's see, the product rule says that
[tex](f*g)' = f'*g + f*g'[/tex]

This looks good.
[tex]y(x)=(12x^6)(7x^4+6)=[/tex]
[tex](12x^6)'(7x^4+6)+(12x^6)(7x^4+6)'=[/tex]

Then you differentiate, looks good.
[tex](72x^5)(7x^4+6)+(12x^6)(28x^3)=[/tex]

Now you simplify.
[tex]504x^9+432x^5+336x^9=[/tex]
[tex]y(x)=840x^9+432x^5[/tex]

Looks good so far, the only thing that I would do, is factor out a 24x^5 at the end there, but you are correct either way.
 
  • #4
33,632
5,287
You'll probably notice that your post was moved from the Precalc section to this one. This is the right place for Calculus homework problems.
 
  • #5
Okay thats fine, LaTex is awesome.
 

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