A) \[\sec {{\text{h}}^{2}}x\]
B) \[\text{cosec}{{\text{h}}^{2}}x\]
C) \[-\sec \,{{\text{h}}^{2}}x\]
D) \[-\text{cosec}{{\text{h}}^{2}}x\]
Correct Answer: D
Solution :
\[y=\frac{{{e}^{x}}+{{e}^{-x}}}{{{e}^{x}}-{{e}^{-x}}}=\frac{\frac{{{e}^{x}}+{{e}^{-x}}}{2}}{\frac{{{e}^{x}}-{{e}^{-x}}}{2}}=\frac{\cosh x}{\sinh x}=\coth \,x\] \[\frac{dy}{dx}=-\text{cosec}{{\text{h}}^{\text{2}}}x\].
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