One of the popular activation functions used in hidden layers of multilayer perceptrons

is the sigmoid function given by

sigmoid$(a)=\frac{1}{1+\text{e}\text{x}\text{p}(-a)},$

where the derivative of the sigmoid function with respect to its parameter is found

as sigmoid$($a$)(1-$sigmoid$($a$)).$ Another popular activation function is the hyperbolic

tangent function given by

$tanh(a)=\frac{\text{e}\text{x}\text{p}(a)-\text{e}\text{x}\text{p}(-a)}{\text{e}\text{x}\text{p}(a)+\text{e}\text{x}\text{p}(-a)}$

$($a$)$ Find the derivative of the hyperbolic tangent function with respect to its pa$-$

rameter. $(10$ points$)$

$($b$)$ What might be the advantage of using the hyperbolic tangent function over

the sigmoid function? $(5$ points$)$