![]() ![]() We state this idea formally in a theorem. ![]() Part of the reason is that the notation takes a little getting used to. The Composite function u o v of functions u and v is. The Chain Rule is a common place for students to make mistakes. Chain rule is a formula for solving the derivative of a composite of two functions. It will also handle compositions where it wouldn't be possible to multiply it out. Since rectangles that are "too big", as in (a), and rectangles that are "too little," as in (b), give areas greater/lesser than \(\displaystyle \int_1^4 f(x)\,dx\), it makes sense that there is a rectangle, whose top intersects \(f(x)\) somewhere on \(\), whose area is exactly that of the definite integral. The Chain Rule is a little complicated, but it saves us the much more complicated algebra of multiplying something like this out. \): Differently sized rectangles give upper and lower bounds on \(\displaystyle \int_1^4 f(x)\,dx\) the last rectangle matches the area exactly.įinally, in (c) the height of the rectangle is such that the area of the rectangle is exactly that of \(\displaystyle \int_0^4 f(x)\,dx\). Practice- Chain Rule Differentiate each function with respect to x. ![]()
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