Derivative of one function with respect to another: (du/dx) / (dv/dx)

1. A.
   $\frac{2\sin x\cos^{2}x}{e^{\cos x}}$
2. B.
   $\frac{2\cos x}{e^{\cos x}}$
3. C.
   $\frac{2\sin x}{e^{\cos x}}$
4. D.
   $\frac{-2\cos x}{e^{\cos x}}$

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1. A.
   $\sqrt{xe^{x}}$
2. B.
   $-2\sqrt{x}$
3. C.
   $2\sqrt{x}e^{x}$
4. D.
   $\frac{1}{2}\sqrt{x}e^{x}$

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1. A.
   $-\dfrac{80}{\sqrt{41}}$
2. B.
   $\dfrac{80}{\sqrt{41}}$
3. C.
   $\frac{12}{5}$
4. D.
   $-\frac{12}{5}$

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1. A.
   1
2. B.
   $\frac{1 + \left( \tan^{- 1}x \right)^{2}}{\left( 1 + \tan^{- 1}x \right)^{2}}$
3. C.
   $\frac{\tan^{- 1}x}{\left( 1 + \tan^{- 1}x \right)^{2}}$
4. D.
   $\frac{1}{\left( 1 + \tan^{- 1}x \right)^{2}}$

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1. A.
   $\frac{1}{1 + K^{\cos^{- 1}x}}$
2. B.
   $\frac{- 1}{1 + K^{\cos^{- 1}x}}$
3. C.
   $\frac{1}{\left( 1 + K^{\cos^{- 1}x} \right)^{2}}$
4. D.
   $\frac{- 1}{\left( 1 + K^{\cos^{- 1}x} \right)^{2}}$

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1. A.
   u
2. B.
   v
3. C.
   $\frac{- 1}{u}$
4. D.
   $\frac{- 1}{v}$

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1. A.
   $-\log_{10}x^2$
2. B.
   $-(\log_{10}x)^2$
3. C.
   $(\log_x 10)^2$
4. D.
   $\dfrac{x^2}{100}$

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