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PRIMARY

2 - 6

SECONDARY

7 - 10

SENIOR

11 - 12

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Quotient Rule

Theory & Practice Questions.

Lesson

Quotient rule

[Formula]

If

f(x) = U ⁄ V

where u and v are both functions of x, then

 

f '(x) = u'v - v'u/v²

 

Example

Differentiate

x² + 1 / x-1

 

Solution

Recall that if f(x) = U ⁄ Vwhere u and v are both functions of x, then f '(x) = u'v - v'u/v²

u = x² + 1      v = x-1

u' = 2x           v' = 1

 

Using this, we get

 

(2x(x-1)-(1)(x^2+1))/(x-1)^2

 

Question

Differentiate the function

y=(x-2)/(x+1)^2

 

Explanation

Use the quotient rule of differentiation, which says that if f(x) = U ⁄ Vwhere u and v are both functions of x, then f '(x) = u'v - v'u/v²

u = x - 2      v = (x+1)²

u' = 1           v' = 2(x+1)

Using the formula, we have

f^' (x)=((x+1)^2-2(x-2)(x+1))/(x+1)^4

((x+1)-2(x-2))/(x+1)^3

 

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