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QLDMath MethodsQuick questions

Unit 2: Calculus

Quick questions on Differentiation of polynomials and tangent lines (QCE Math Methods Unit 2)

8short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is power rule?
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For any rational nn:
What is sum rule?
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The derivative of a sum is the sum of the derivatives:
What is constant multiple rule?
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A constant pulls outside the derivative:
What is constant function?
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The derivative of a constant is zero:
What is coefficient times power?
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ddx(5x3)=5⋅3x2=15x2\dfrac{d}{dx} (5 x^3) = 5 \cdot 3 x^2 = 15 x^2.
What is negative power?
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ddx(x−2)=−2x−3=−2/x3\dfrac{d}{dx} (x^{-2}) = -2 x^{-3} = -2/x^3.
What is rational power?
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ddx(x1/2)=12x−1/2=1/(2x)\dfrac{d}{dx} (x^{1/2}) = \tfrac{1}{2} x^{-1/2} = 1/(2 \sqrt x).
What is combine terms before differentiating?
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Expand brackets and split fractions if needed. For x3−2xx\dfrac{x^3 - 2x}{x}, first simplify to x2−2x^2 - 2, then differentiate to 2x2x.

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