...form = ^ ~gh . (1.45) As usually expressed in words [hardly mathematically, but sufficiently clearly]; The derivative of a quotient is equal to 'the bottom...the bottom, all over the bottom squared'. Find the (first) derivatives of the following: sin x 3x2 + 1x + \ (c) tan x in the form , (a) — cos x 8x2...

...derivative of a quotient equals the bottom (denominator) times the derivative of the top (numerator) minus the top times the derivative of the bottom all over the bottom squared." The quotient of two functions can always be expressed as a product of two functions: Consequently,...

...that we have the product rule and the next two rules. RULE 8 The quotient rule. The quotient rule says the bottom times the derivative of the top minus the top times the derivative of the bottom, all divided by the bottom squared. EXAMPLE 9 Findy'ify = -r x2 x3 + 2x + l (bottom)(top)' , _ (x3 + 2x...

...the derivative of the first. The derivative is given by the top times the derivative of the bottom minus the top times the derivative of the bottom all over the bottom squared. Function of a function: dx dg dx dx The derivative is given by the derivative of the brackets times...

...If y = — then the derivative is — = — — — . v dx v2 You may choose to remember the rule as 'bottom times the derivative of the top, minus the top times the derivative of the bottom, divided by the bottom squared'. _--r-3 dy _(2x-l)x2x-(x2-3)x2 ™*JT У~2х-1 ' dx~ (2x-l)2 _4x2-2x-2x2+6...

...[g(x)]z The Basics 39 RULE 8 40 BOB MILLER'S HIGH SCHOOL CALCULUS FORTHE CLUELESS The quotient rule says the bottom times the derivative of the top minus the top times the derivative of the bottom, all divided by the bottom squared. EXAMPLE 10 — Find y' if y = (bottom)(top)' - (top)(bottom) y = x3...