A) \[\frac{-8}{{{({{e}^{2x}}-{{e}^{-2x}})}^{2}}}\]
B) \[\frac{8}{{{({{e}^{2x}}-{{e}^{-2x}})}^{2}}}\]
C) \[\frac{-4}{{{({{e}^{2x}}-{{e}^{-2x}})}^{2}}}\]
D) \[\frac{4}{{{({{e}^{2x}}-{{e}^{-2x}})}^{2}}}\]
Correct Answer: A
Solution :
\[y=\frac{{{e}^{2x}}+{{e}^{-2x}}}{{{e}^{2x}}-{{e}^{-2x}}}\] \[\therefore \frac{dy}{dx}=\frac{({{e}^{2x}}-{{e}^{-2x}})2({{e}^{2x}}-{{e}^{-2x}})-({{e}^{2x}}+{{e}^{-2x}})2({{e}^{2x}}+{{e}^{-2x}})}{{{({{e}^{2x}}-{{e}^{-2x}})}^{2}}}\] \[=\frac{-8}{{{({{e}^{2x}}-{{e}^{-2x}})}^{2}}}\].You need to login to perform this action.
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