The Chain Rule
www.mathcentre.ac.uk › uploaded › mc-ty-chain-2009-1The chain rule states dy dx = dy du × du dx In what follows it will be convenient to reverse the order of the terms on the right: dy dx = du dx × dy du which, in terms of f and g we can write as dy dx = d dx (g(x))× d du (f(g((x))) This gives us a simple technique which, with some practice, enables us to apply the chain rule directly Key Point
03 - Chain Rule
https://cdn.kutasoftware.com/Worksheets/Calc/03 - Chain Rule.pdfDifferentiation - Chain Rule Date_____ Period____ Differentiate each function with respect to x. 1) y = (x3 + 3)5 dy dx = 5(x3 + 3)4 ⋅ 3x2 = 15 x2(x3 + 3)4 2) y = (−3x5 + 1)3 dy dx = 3(−3x5 + 1)2 ⋅ −15 x4 = −45 x4(−3x5 + 1)2 3) y = (−5x 3 − 3) dy dx = 3(−5x3 − 3)2 ⋅ −15 x2 = −45 x2(−5x3 − 3)2 4) y = (5x2 + 3)4 dy ...
THE CHAIN RULE IN PARTIAL DIFFERENTIATION
wwwf.imperial.ac.uk › ~jdg › AECHAIN2 Chain rule for two sets of independent variables If u = u(x,y) and the two independent variables x,y are each a function of two new independent variables s,tthen we want relations between their partial derivatives. 1. When u = u(x,y), for guidance in working out the chain rule, write down the differential δu= ∂u ∂x δx+ ∂u ∂y δy ...
03 - Chain Rule
cdn.kutasoftware.com › Worksheets › Calc13) Give a function that requires three applications of the chain rule to differentiate. Then differentiate the function. Many answers: Ex y = (((2x + 1)5 + 2) 6 + 3) 7 dy dx = 7(((2x + 1)5 + 2) 6 + 3) 6 ⋅ 6((2x + 1)5 + 2) 5 ⋅ 5(2x + 1)4 ⋅ 2-2-Create your own worksheets like this one with Infinite Calculus. Free trial available at ...