how is the formula for the derivative of a quotient of two functions derived?

[mighty urchin]

derivative of f(x)/g(x) ?

[obsidian marsh]

derivative of f(x)/g(x)?

[finite coyote]

It is derived from the chain rule, the derivative of something to the power of a real number and from the derivative of the product of two functions. Unless you wanna know where those came from as well. $f(x)/g(x)=f(x) (g(x))^{-1}$ whose derivative is $$f'(x)(g(x))^{-1} + f(x)((g(x))^{-1})' = \frac{f'(x)g(x)}{(g(x))^2} + f(x)\times\frac{-1\times g'(x)}{(g(x))^2}$$ $$= \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}$$

[wind oxide]

Pyrodynamic