# Applying Product Rule

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

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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.

Thanks for the response

Mark44
Mentor
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.

Okay thats fine, LaTex is awesome.