Last updated on Sep 20, 2026

Differentiating Where n is a Negative Integer (VCE SSCE Mathematical Methods): Quizzes

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Differentiating Where n is a Negative Integer

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What does the notation $\mathbb{R} \setminus \{0\}$ mean?

All real numbers except zero

What is the derivative of $f(x) = x^{-4}$ ?

$f'(x) = -4x^{-5}$

How do you rewrite $\frac{1}{x^2}$ using negative powers?

$x^{-2}$

When $n$ is negative in $f(x) = x^n$ , what is the domain?

$\mathbb{R} \setminus \{0\}$

What is the derivative of a constant $c$ ?

$0$

Find $f'(x)$ for $f(x) = x^{-1} + 2$ .

$f'(x) = -x^{-2}$

What is $f'(1)$ if $f(x) = x^2 + x^{-1}$ ?

$1$

Find the derivative of $2x^{-3}$ .

$-6x^{-4}$

Why is $x^4$ positive for all $x \neq 0$ ?

Any number to an even power is positive

Why is $f'(x) = \frac{-3}{x^4}$ always negative for $x \neq 0$ ?

$x^4$ is positive, so $\frac{-3}{x^4} < 0$

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