Calculate the derivative of y = sinh 1

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H OMEWORK 6 S OLUTIONS Math 1910, Fall 2019 7.7.30 Calculate the derivative of y = sinh 1 ( x 2 + 1 ) .
7.7.33 Show that for any constants M , k , and a , the function y ( t ) = 1 2 M 1 + tanh k ( t - a ) 2 satisfies the logistic equation : y 0 y = k ( 1 - y M ) .
7.7.40 Prove the formula: d dt cosh - 1 t = 1 t 2 - 1 for t > 1 .
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7.7.49 (a) Show that y = tanh ( t ) satisfies the differential equation dy / dt = 1 - y 2 with initial condition y ( 0 ) = 0 .

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