Rules for Differentiation (Grade 12 NSC Matric Mathematics): Flashcards

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Rules for Differentiation
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Power rule: ddx[xn]\frac{d}{dx}[x^n]

nxn−1nx^{n-1}

ddx[k]\frac{d}{dx}[k] where kk is constant

00

ddx[k⋅f(x)]\frac{d}{dx}[k \cdot f(x)]

k⋅f′(x)k \cdot f'(x)

Sum rule: ddx[f(x)+g(x)]\frac{d}{dx}[f(x) + g(x)]

f′(x)+g′(x)f'(x) + g'(x)

Difference rule: ddx[f(x)−g(x)]\frac{d}{dx}[f(x) - g(x)]

f′(x)−g′(x)f'(x) - g'(x)

ddx[x5]\frac{d}{dx}[x^5]

5x45x^4

ddx[3x2]\frac{d}{dx}[3x^2]

6x6x

What happens to constants when differentiating

They disappear (derivative is zero)

When to use first principles

When question explicitly asks for it

How to write final derivative answers in exams

With positive exponents

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