A) \[\frac{1}{1+{{a}^{{{\cos }^{-1}}x}}}\]
B) \[-\frac{1}{1+{{a}^{{{\cos }^{-1}}x}}}\]
C) \[\frac{1}{{{(1+{{a}^{{{\cos }^{-1}}x}})}^{2}}}\]
D) None of these
Correct Answer: C
Solution :
\[y=\frac{{{a}^{{{\cos }^{-1}}x}}}{1+{{a}^{{{\cos }^{-1}}x}}},\,\,\,z={{a}^{{{\cos }^{-1}}x}}\] \[\Rightarrow y=\frac{z}{1+z}\] \[\Rightarrow \frac{dy}{dz}=\frac{(1+z)1-z(1)}{{{(1+z)}^{2}}}=\frac{1}{{{(1+z)}^{2}}}\]\[=\frac{1}{{{(1+{{a}^{{{\cos }^{-1}}x}})}^{2}}}\].You need to login to perform this action.
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