8. Differentiation
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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