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Calculus, 2ADV C3 2024 MET1 1a

Let  \(y=e^x \cos\,3 x\).

Find  \(\dfrac{d y}{d x}\)   (2 marks)

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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 14

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)?`

  1. `-sec x`
  2. `-tan x`
  3. `sec x`
  4. `tan x`
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`B`

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

  
`=>  B`