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

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Differentiating Where n is a Negative Integer
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xnx^{-n} equals

1xn\frac{1}{x^n}

R{0}\mathbb{R} \setminus \{0\} means

All real numbers except zero

Why exclude 0 from domain with negative powers?

Division by zero is undefined

Power rule: derivative of xnx^n

nxn1nx^{n-1}

Derivative of constant cc

00

Domain when nn is negative

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

1x\frac{1}{x} as negative power

x1x^{-1}

Derivative of x3x^{-3}

3x4-3x^{-4}

Sign of x4x^4 for x0x \neq 0

Positive

Before differentiating, rewrite fractions as

Negative powers

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