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Standard Level

11.10 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
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