going to start you know complexifying a bit so now we have a function here with output variable d that is a function of three scalar inputs a b and c so a b and c are some specific values three inputs into our expression graph and a single output d and so if we just print d we get four and now what i like to do is i'd like to again look at the derivatives of d with respect to a b and c and uh think through uh again just the intuition of what this derivative is telling us so in order to evaluate this derivative we're going to get a bit hacky here we're going to again have a very small value of h and then we're going to fix the inputs at some values that we're interested in so these are the this is the point a b c at which we're going to be evaluating the the derivative of d with respect to all a b and c at that point so there are the inputs and now we have d1 is that expression and then we're going to for example look at the derivative of d with respect to a so we'll take a and we'll bump it by h and then we'll get d2 to be the exact same function and now we're going to print um you know f1 d1 is d1 d2 is d2 and print slope so the derivative or slope here will be um of course d2 minus d1 divide h so d2 minus d1 is how much the function increased uh when we bumped the uh the specific input that we're interested in by a tiny amount and this is the normalized by this is the normalized by h to get the slope so um yeah so this so i just run this we're going to print d1 which we know is four now d2 will be bumped a will be bumped by h so let's just think through a little bit uh what d2 will be uh printed out here in particular d1 will be four will d2 be a number slightly greater than
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