Differentiating the Trigonometric Functions (HSC SSCE Mathematics Advanced): Quizzes

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Differentiating the trigonometric functions
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What is ddxsin⁡x\frac{d}{dx} \sin x?

cos⁡x\cos x

What is ddxtan⁡x\frac{d}{dx} \tan x?

sec⁡2x\sec^2 x

In what units must xx be measured for the standard trig derivatives to work?

Radians

What is ddxcos⁡(5x−1)\frac{d}{dx} \cos(5x - 1)?

−5sin⁡(5x−1)-5\sin(5x - 1)

What is ddxtan⁡2x\frac{d}{dx} \tan^2 x?

2tan⁡xsec⁡2x2\tan x \sec^2 x

What is ddx(excos⁡x)\frac{d}{dx}(e^x \cos x)?

ex(cos⁡x−sin⁡x)e^x(\cos x - \sin x)

What is ddx(sin⁡xx)\frac{d}{dx}\left(\frac{\sin x}{x}\right)?

xcos⁡x−sin⁡xx2\frac{x\cos x - \sin x}{x^2}

What is the second derivative of y=sin⁡xy = \sin x?

−sin⁡x-\sin x

What is the gradient of the tangent to y=sin⁡xy = \sin x at the origin?

11

What is the period of y=tan⁡xy = \tan x?

π\pi

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