How do I Apply the Product Rule in Calculus?

[Jake Minneman]

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.
y(x)=(12x^6)(7x^4+6)=
(12x^6)'(7x^4+6)+(12x^6)(7x^4+6)'=
(72x^5)(7x^4+6)+(12x^6)(28x^3)=
504x^9+432x^5+336x^9=
y(x)=840x^9+432x^5

 

[QuarkCharmer]

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.
y(x)=(12x^6)(7x^4+6)=
(12x^6)'(7x^4+6)+(12x^6)(7x^4+6)'=
(72x^5)(7x^4+6)+(12x^6)(28x^3)=
504x^9+432x^5+336x^9=
y(x)=840x^9+432x^5

Let's see, the product rule says that
(f*g)' = f'*g + f*g'

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

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

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

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.

 

[Jake Minneman]

Thanks for the response

 

[Mark44]

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.

 

[Jake Minneman]

Okay that's fine, LaTex is awesome.