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2.04 The quotient rule

Interactive practice questions

Consider the function $y=\frac{3}{x}$y=3x.

a

By first re-writing with a negative index, find $\frac{dy}{dx}$dydx.

$y=3x^{\editable{}}$y=3x

$\frac{dy}{dx}=\editable{}x^{\editable{}}$dydx=x

b

Use the quotient rule to differentiate $y=\frac{3}{x}$y=3x.

$\frac{dy}{dx}=\frac{x\times\left(\editable{}\right)-3\times\left(\editable{}\right)}{x^{\editable{}}}$dydx=x×()3×()x

$\frac{dy}{dx}=\editable{}$dydx=

c

In which two quadrants of the number plane does the hyperbola $y=\frac{3}{x}$y=3x exist?

$I$I

A

$II$II

B

$III$III

C

$IV$IV

D
d

For what value of $x$x is the gradient of $y$y undefined?

Easy
2min

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

Easy
4min

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

Easy
6min

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

Easy
2min
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Outcomes

3.2.4.1

select and apply the product rule, quotient rule and chain rule to differentiate functions; express derivatives in simplest and factorised form

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