When x represents a variable, the hyperbolic secant function is written as sech ? x in mathematical form. The derivative of the hyperbolic secant function. Prove the following formula for the derivative of the hyperbolic secant, [ D(operatorname{sech} x) = -operatorname{. To prove the derivative of coshx, we will use the following formulas: sinhx = (ex – e-x)/2 cosh x = (ex + e-x)/2 d(ex)/dx = e. d(e-x)/dx = -e. Hence, we. The hyperbolic secant function is mathematically written as sech ? x when x is used to represent a variable. The differentiation or the derivative of. sin x = cos x. Proof, csc x = -csc x cot x. Proof. cos x = – sin x. cosh x = sinh x. Proof, sech x = – tanh x sech x. Proof. tanh x = 1 – tanh2 x

## derivative of sech^-1(x)

## derivative of sech x tanh x

## integration of sech(x)

## tanh x derivative