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Question

Assuming the derivatives of sinhx and coshx, use the quotient rule to prove that if y=tanhx=sinhxcoshx then dydx=sech2x.

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Solution

tanhx=exexex+ex

now,

d(exexex+ex)dx=(ex+ex)(ex+ex)(exex)(exex)(ex+ex)2

4(ex+ex)2=sech2x

hence,

d(tanhx)dx=sech2x

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