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QLDMath MethodsQuick questions

Unit 2: Calculus

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

12short 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 $n$:
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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$\dfrac{d}{dx} (5 x^3) = 5 \cdot 3 x^2 = 15 x^2$.
What is negative power?
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$\dfrac{d}{dx} (x^{-2}) = -2 x^{-3} = -2/x^3$.
What is rational power?
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$\dfrac{d}{dx} (x^{1/2}) = \tfrac{1}{2} x^{-1/2} = 1/(2 \sqrt x)$.
What is combine terms before differentiating?
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Expand brackets and split fractions if needed. For $\dfrac{x^3 - 2x}{x}$, first simplify to $x^2 - 2$, then differentiate to $2x$.
What is forgetting to drop the power by one?
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$\dfrac{d}{dx} x^4 = 4 x^3$, not $4x^4$.
What is misapplying the rule to a constant times $x$?
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$\dfrac{d}{dx} (3x) = 3$, not $3x$ or $3 x^0$ stated awkwardly.
What is confusing tangent with secant?
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A secant joins two points on the curve; a tangent touches at one. The derivative gives the tangent gradient.
What is forgetting the negative-reciprocal rule for normals?
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$m_{\text{normal}} = -1/m_{\text{tangent}}$. A common slip is using $-m_{\text{tangent}}$ or $1/m_{\text{tangent}}$.

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