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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x−nx^{-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

nxn−1nx^{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

x−1x^{-1}

Derivative of x−3x^{-3}

−3x−4-3x^{-4}

Sign of x4x^4 for x≠0x \neq 0

Positive

Before differentiating, rewrite fractions as

Negative powers

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