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VICMath MethodsQuick questions

Unit 2: Functions, calculus and probability

Quick questions on Derivatives of trigonometric functions (VCE Maths Methods Unit 2)

5short 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 trig times polynomial?
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Product rule. ddx(xsin⁡x)=sin⁡x+xcos⁡x\frac{d}{dx} (x \sin x) = \sin x + x \cos x.
What is squared trig?
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Chain rule with u2u^2. ddxsin⁡2x=2sin⁡xcos⁡x=sin⁡2x\frac{d}{dx} \sin^2 x = 2 \sin x \cos x = \sin 2x.
What is q1?
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Differentiate f(x)=cos⁡(5x)f(x) = \cos(5x) and g(x)=tan⁡(3x)g(x) = \tan(3x). [2+2 marks]
What is q2?
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Find the derivative of y=xcos⁡xy = x\cos x. [3 marks]
What is q3?
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A particle's displacement is s(t)=2sin⁡(3t)s(t) = 2\sin(3t) m. (a) Find the velocity v(t)v(t). (b) Find the velocity at t=0t = 0.

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