Derivatives of Trig Functions Practice

Sample questions

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1. Sample 1difficulty 1/5

   $\dfrac{d}{dx}\sin x =$

   • A

     $\sec^2 x$

   • B

     $\cos x$

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   • C

     $-\cos x$

   • D

     $-\sin x$

   Why

   Standard derivative.

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2. Sample 2difficulty 1/5

   $\dfrac{d}{dx}\cos x =$

   • A

     $-\cos x$

   • B

     $\sin x$

   • C

     $\sec x \tan x$

   • D

     $-\sin x$

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   Why

   Standard derivative.

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3. Sample 3difficulty 2/5

   $\dfrac{d}{dx}\cot x =$

   • A

     $-\sec x \csc x$

   • B

     $\csc^2 x$

   • C

     $-\csc^2 x$

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   • D

     $\sec^2 x$

   Why

   Standard derivative.

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4. Sample 4difficulty 2/5

   $\dfrac{d}{dx}\tan x =$

   • A

     $-\cot x$

   • B

     $\sec^2 x$

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   • C

     $\sec x$

   • D

     $\cot x$

   Why

   $\tan = \sin/\cos$; quotient rule gives $\sec^2 x$.

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5. Sample 5difficulty 2/5

   $\dfrac{d}{dx}\sec x =$

   • A

     $\sec^2 x$

   • B

     $\sec x \tan x$

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   • C

     $-\sec x \tan x$

   • D

     $\tan x$

   Why

   Standard derivative: $\sec x \tan x$.

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