Differentiating Inverse Trig Functions Practice

Sample questions

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1. Sample 1difficulty 2/5

   $\dfrac{d}{dx}\arctan(2x) =$

   • A

     $\dfrac{1}{1+4x^2}$

   • B

     $\dfrac{2x}{1+4x^2}$

   • C

     $\dfrac{2}{1+x^2}$

   • D

     $\dfrac{2}{1+4x^2}$

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   Why

   $\dfrac{1}{1+(2x)^2} \cdot 2 = \dfrac{2}{1+4x^2}$.

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2. Sample 2difficulty 2/5

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

   • A

     $\dfrac{1}{\sqrt{1-x^2}}$

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   • B

     $\dfrac{1}{\cos x}$

   • C

     $\dfrac{-1}{\sqrt{1-x^2}}$

   • D

     $\dfrac{1}{1+x^2}$

   Why

   Standard inverse trig derivative.

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3. Sample 3difficulty 2/5

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

   • A

     $\dfrac{1}{1+x^2}$

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   • B

     $\dfrac{1}{\sqrt{1-x^2}}$

   • C

     $\dfrac{1}{1-x^2}$

   • D

     $\sec^2 x$

   Why

   Standard inverse trig derivative.

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4. Sample 4difficulty 2/5

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

   • A

     $\dfrac{1}{1+x^2}$

   • B

     $\dfrac{-1}{\sqrt{1-x^2}}$

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   • C

     $\dfrac{1}{\sqrt{1-x^2}}$

   • D

     $\dfrac{-1}{1+x^2}$

   Why

   Standard derivative — note the negative sign.

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5. Sample 5difficulty 3/5

   $\dfrac{d}{dx}\arctan(x^2) =$

   • A

     $\dfrac{1}{1 + x^4}$

   • B

     $\dfrac{2x}{1 + x^4}$

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   • C

     $\dfrac{2x}{(1 + x^2)^2}$

   • D

     $\dfrac{2}{1 + x^2}$

   Why

   $\dfrac{1}{1 + (x^2)^2} \cdot 2x = \dfrac{2x}{1 + x^4}$.

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