New Zealand
Level 8 - NCEA Level 3

# Quotient Rule

## Interactive practice questions

Suppose we want to differentiate $y=\frac{2x-5}{5x-2}$y=2x55x2 using the quotient rule.

a

Using the substitution $u=2x-5$u=2x5, find $u'$u.

b

Using the substitution $v=5x-2$v=5x2, find $v'$v.

c

Hence find $y'$y.

d

Is it possible for the derivative of this function to be zero?

No

A

Yes

B

No

A

Yes

B
Easy
Approx 5 minutes

Suppose we want to differentiate $y=\frac{5x^2}{2x+8}$y=5x22x+8 using the quotient rule.

Suppose we want to differentiate $y=\frac{3x}{5x-4}$y=3x5x4 using the quotient rule.

Suppose we want to differentiate $y=\frac{4x+3}{4x-3}$y=4x+34x3 using the quotient rule.

### Outcomes

#### M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

#### 91578

Apply differentiation methods in solving problems