NZ Level 7 (NZC) Level 2 (NCEA)
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Power Rule (x^n)

Interactive practice questions

Consider the function $f\left(x\right)=x^n$f(x)=xn, where $n$n is any positive integer.

Complete the following table. (Use the ^ key to create powers).

$f\left(x\right)$f(x) $f'\left(x\right)$f(x)
$x$x $\editable{}$
$x^2$x2 $\editable{}$
$x^3$x3 $\editable{}$
$x^4$x4 $\editable{}$
$x^n$xn $\editable{}$
Easy
Approx a minute
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Determine the derivative of $y=-6$y=6 with respect to $x$x.

Determine the derivative of $y=x^7$y=x7.

Determine the derivative of $y=x^{-7}$y=x7.

Outcomes

M7-10

Apply differentiation and anti-differentiation techniques to polynomials

91262

Apply calculus methods in solving problems

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