smc-967-80-Trig Overlap

Calculus, 2ADV C3 2024 MET1 1a

Let \(y=e^x \cos\,3 x\).

Find \(\dfrac{d y}{d x}\) (1 mark)

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\(e^x (\cos(3x)-3\sin(3x))\)

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	\(y\)	\(=e^x \cos(3x)\)
	\(\dfrac{dy}{dx}\)	\(=e^x.(-3\sin(3x))+\cos(3x).e^x\)
		\(=e^x(\cos(3x)-3\sin(3x))\)

Calculus, 2ADV C2 EQ-Bank 2

Differentiate with respect to `x`:

`e^(tan(2x))` (2 marks)

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`2 sec^2(2x)* e^(tan(2x))`

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`y`	`=e^(tan(2x))`
`dy/dx`	`= d/(dx)tan(2x) xx e^(tan(2x))`
	`= 2 sec^2(2x)* e^(tan(2x))`

Calculus, 2ADV C2 2016 HSC 5 MC

What is the derivative of `ln (cos x)?`

`– sec x`
`– tan x`
`sec x`
`tan x`

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`B`

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`y`	`= ln (cos x)`
`(dy)/(dx)`	`= (-sin x)/(cos x)`
	`= -tan x`

`=> B`