Compute the derivatives df/dx of the following functions. Describe your steps in detail.

a. Use the chain rule, Provide the dimensions of every single partial derivative.

f(z) = exp(-1/2z)

z = g(y) = y^Ts^–¹y

y=h(x) = x-μ

where x, μ∈R^D, S∈R^DxD.

b. Use the chain rule, Provide the dimensions of every single partial derivative. You do not need to compute the product of the partial derivatives explicitly.

f = tanh(z)∈R^M

z = Ax+b, x∈R^N, A∈R^MxN, b∈R^M

Here, tanh is applied to every component of z.