265L11 - LESSON 11 The Chain Rules READ Section 15.6 NOTES...

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LESSON 11 The Chain Rules READ: Section 15.6. NOTES: Back in Calculus I, you learned the chain rule , which is used to compute the derivative of a composite function: ( f ( g ( x ))) 0 = f 0 ( g ( x )) g 0 ( x ) or, using the Leibniz notation, if y = f ( x ) and x = g ( t ), then the rate of change of y with respect to t is given by dy dt = dy dx dx dt . The Chain Rule was extended to paths in section 15.5. This section is devoted to the general form of the Chain Rule. The extension of this rule to functions of several variables is pretty easy to state and to use. For example, suppose w = f ( x,y,z ) is a function of three variables, and that each of those three is in turn functions of, say, two variables s and t . Let’s write x = x ( s,t ), y = y ( s,t ), and z = z ( s,t ). If you imagine the formulas for x , y and z in terms of s and t plugged into the function f , then you can see that w can be thought of as a function of s and t . For example, if w = xy + z , and x = s + t , y = st and
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This note was uploaded on 02/24/2011 for the course MATH 265 taught by Professor Jerrymetzger during the Winter '11 term at North Dakota.

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265L11 - LESSON 11 The Chain Rules READ Section 15.6 NOTES...

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