Quotient rule
(u/v)' = (u'v − uv') / v². For quotients.
Y13 differentiation. Sometimes simpler to rewrite as a product (u × v-1) and use the product+chain rules.
Worked examples
y = x / (x+1): y' = (1·(x+1) − x·1)/(x+1)² = 1/(x+1)².
y = sin x / x: y' = (x cos x − sin x) / x².
y = ex/x²: y' = (ex·x² − ex·2x)/x&sup4; = ex(x−2)/x³.
Frequently asked questions
Quotient rule mnemonic?
‘Low D-high minus high D-low, all over the square of what's below.’
Simplify v²?
Yes — often algebra simplifies after applying.