![]() Of these orange parentheses I would put it inside of Times that something squared times the derivative with respect to X of that something, in this case, the something is sin, let me write that in the blue color, it is sin of X squared. Something to the third power with respect to that something. So, if we apply the chain rule it's gonna be theĭerivative of the outside with respect to the inside or the something to the third power, the derivative of the And so, one way to tackle this is to apply the chain rule. Outside of this expression we have some business in here that's being raised to the third power. ![]() This isn't a straightforwardĮxpression here but you might notice that I have something being raised to the third power, in fact, if we look at the Of this with respect to X? What is DY/DX which weĬould also write as Y prime? Well, there's a couple of Squared to the third power, which of course we could also write as sin of X squared to the third power and what we're curious about is what is the derivative I've spent a lot of time on this and now I think it is starting to make sense. And finally multiplies the result of the first chain rule application to the result of the second chain rule application.Įarlier in the class, wasn't there the distinction between outside and inside of an expression? Here we apply the chain rule to the outside first (the cube function), and secondly we apply it to the inside function, the sin(x^2). He then goes on to apply the chain rule a second time to what is inside the parentheses of the original expression. Applying the product rule is the easy part. ![]() So, I think what he is saying is let u = everything which is inside the parentheses, then we have y = u^3, dy/du = 3 u^2 = 3 times (everything inside the parentheses) squared. Where Sal draws a parenthesis and says something goes in there seems to gloss over a little bit how the chain rule entity is identified and then goes in there, and next he says to apply the product rule. ![]() The video is about applying the chain rule twice, there may be other ways to get the answer, but first I want to understand how to apply the chain rule twice, which can be confusing. ![]()
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