Question #1712

Find the derivative. Simplify if possible.
f(t) = (sech(9e power t))2

Expert's answer

sech(z) = 2 (e^{z} + e^{-z})^{-1};[sech(z)]' = - 2 (e^{z} - e^{-z})/(e^{z} + e^{-z})^{2} = - sech(z) tanh(z);

f'(t) = 2 [sech (9e^{t})]' sech(9e^{t}) = - 2 [9e^{t}]' sech^{2} (9e^{t}) tanh(9e^{t}) = - 18 e^{t} sech^{2} (9e^{t}) tanh(9e^{t})

f'(t) = 2 [sech (9e

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