Hey.

I was not able to make the class where the explained the quotient rule in calculus.

I'm trying to self learn it but the book isn't helping that much.

They're trying to find the derivative of:

$\displaystyle y\prime=\frac{x^2+x-2}{x^3+6}$

They use the Quotient Rule Formula to get to

$\displaystyle y\prime=\frac{{(x^3+6)}{\frac{d}{dx}}{(x^2+x-2)}-{(x^2+x-2)}{\frac{d}{dx}}{(x^3+6)}}{{(x^3+6)}^2}$

Thats all well and good, but then they make the jump from that to:

$\displaystyle y\prime=\frac{(x^3+6)(2x+1)-(x^2+x-2)(3x^2)}{(x^3+6)^2}$

And then they just simplify that to:

$\displaystyle y\prime=\frac{-x^4-2x^3+6x^2+12x+6}{(x^3+6)^2}$

But can someone explain that first jump?

Thanks!