Question

in Quotient rule of differentiation :

i'm talking about the nominator
which one is correct :

(top' * bottom )- (top * bottom' )
(bottom * top' ) - ( top * bottom' )

another one :)

is 8x^2-40x-12 equal to -8x^2 +40x+12 ?

thanx :)

Answer 1

Not that bad to figure out oneself. :P\[\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{d}{dx}\left(f(x)g(x)^{-1}\right)=f'(x)g(x)^{-1}-f(x)g'(x)g(x)^{-2}\]\[\frac{f'(x)}{g(x)}-\frac{f(x)g'(x)}{g(x)^2}=\frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}\]Voila!

Also, no, those two polynomial equations don't equal.

Answer 2

the graphs are different, but their roots (if there are any) are the same