$($d$)$ The sigmoid function is a commonly used continuous activation function.

$(x)=\frac{1}{1+e^{-x}}$

$($i$)$ Sketch the sigmoid function.

$($ii$)$ Explain one property of the sigmoid function that is necessary for training with Gradient

Descent.

$($iii$)$ The derivative of the sigmoid is $(x)(1-(x)).$ Explain briefly why this is useful for training

multi$-$layer nets with backpropagation.