Question

Prove the quotient rule. hint: you can do this directly, but it may be easier to find the derivative of 1/x and then use the chain rule and the product rule

Answer 1

The quotient rule is
d(u/v) = (u dv - v du) / u2

d(u/v) can written as
d( u (1/v) )

Using the product rule and chain rule
d( u (1/v)) = u d(1/v) + (1/v) du
= u (-1/v2) dv + (!/v) du
= (u dv - v du) / u2