uh printed out here in particular d1 will be four will d2 be a number slightly greater than four or slightly lower than four and that's going to tell us the sign of the derivative so we're bumping a by h b is minus three c is 10 so you can just intuitively think through this derivative and what it's doing a will be slightly more positive and but b is a negative number so if a is slightly more positive because b is negative three we're actually going to be adding less to d so you'd actually expect that the value of the function will go down so let's just see this yeah and so we went from four to 3.9996 and that tells you that the slope will be negative and then um will be a negative number because we went down and then the exact number of slope will be exact amount of slope is negative three and you can also convince yourself that negative three is the right answer um mathematically and analytically because if you have a times b plus c and you are you know you have calculus then uh differentiating a times b plus c with respect to a gives you just b and indeed the value of b is negative three which is the derivative that we have so you can tell that that's correct so now if we do this with b so if we bump b by a little bit in a positive direction we'd get different slopes so what is the influence of b on the output d so if we bump b by a tiny amount in a positive direction then because a is positive we'll be adding more to d right so um and now what is the what is the sensitivity what is the slope of that addition and it might not surprise you that this should be two and why is it two because d of d by db differentiating with respect to b would be would give us a and the value of a is two so that's also working well and then if c gets bumped a tiny amount in h by h then of course a times
rtdocs_stable/api.python.langchain.com/en/stable/modules/indexes/document_loaders/examples/audio.html