Question

what is the derivative of
y=(x^3 + 3)(x^4 + 3)

Answer 1

We can use a derivation formula\[(f(x)g(x))'=f'(x)g(x)+f(x)g'(x)\]

Answer 2

In this problem, f(x)=x^3 + 3 and g(x)=x^4 + 3

Answer 3

So, \[((x^3+3)(x^4+3))'=(x^3+3)'(x^4+3)+(x^3+3)(x^4+3)'=3x^2(x^4+3)+4x^3(x^3+3)=3x^6+9x^2+4x^6+12x^3=10x^6+12x^3+9x^2\]

Answer 4

Sorry about that.

Answer 5

I'll continue off from where it was cut off.

Answer 6

Personally, I think it's easier to distribute it all out.\[y=(x^3+3)(x^4+3)=x^7+3x^4+ 3x^3 + 9\]Now you can just power rule everything and that's it.\[\frac{dy}{dx}=7x^6+12x^3+9x^2\]

Answer 7

Oh yeah

Answer 8

I was going the hard way...

Answer 9

thanks!

Answer 10

@science0229 That's the annoying part about calculus, there's always some simple way to do it but if you don't find it that way, you're probably screwed, lol.

Answer 11

You're welcome