Interactive practice questions
Consider the function $y=\frac{3}{x}$y=3x.
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
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=
In which two quadrants of the number plane does the hyperbola $y=\frac{3}{x}$y=3x exist?
$I$I
$II$II
$III$III
$IV$IV
For what value of $x$x is the gradient of $y$y undefined?
Suppose we want to differentiate $y=\frac{2x-5}{5x-2}$y=2x−55x−2 using the quotient rule.
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=3x5x−4 using the quotient rule.