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

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Mathematics

Iris Washington

13 September, 09:06

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

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Hailee Stein · 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