Question

How does the quotient rule work?

Answer 1

\[\frac{ d }{ dx }\left( \frac{ u }{v } \right)=\frac{ v \frac{ du }{dx }-u \frac{ dv }{dx }}{v ^{2} }\]

Answer 2

You want a proof or the rule itself?

Answer 3

A proof

Answer 4

Its proven by the first principle of derivates. f'(x)=(f(x+h)-f(x))/h

Answer 5

Its only logical as f'(x) is the change in f(x) instantaneously

Answer 6

Here consider the function to be h(x)=F(x)/G(x) and solve using firstprinciple. Its lenghty and a little difficult but you would get the quotient rule from there

Answer 7

Thank you!

Answer 8

(Y)

Answer 9

I can give a proof.

Answer 10

It involves the product rule.