Contributed by Matthew Zak.

- Create a very simple graph(circuit) given with and compute all the derivatives of f with respect to inputs using a chain rule ().
- Show how will the gradient of with respect to change when we increase the input by .
- Having a function where is given by the function above and is is a sigmoid function, compute the derivative of with respect to input .

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I am not sure about the meaning of the word “circuit”, as I do not see how to build a graph with a closed loop from f. Does someone have an explanation ?

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For 2., do you mean the _derivative_ of f with respect to x1, or the gradient of f with respect to _x_?

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I think he talks about the component x1 so I considered the derivative of f w.r.t x1

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Since the gradient of with regards of is a function of . I think he means what is the impact on the gradient.

I think the answer is .

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