Suppose : R R is a function of variables x, y, z, and : R R...

 

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Suppose : R R is a function of variables x, y, z, and : R R is written as [x(u)] g(u)= y(u) [z(u)] Then the composition fois a function of just u. Use the chain rule to come up with an expression for of du Recall that, in terms of total derivatives, the chain rule says roughly that D( o ) = D D or, as matrices [D(f' og)] = [Df] [Dg] Or, to be more precise, using matrices, it says the following: [D('9)]|z, = [D]|g20) [Dg] | do Suppose : R R is a function of variables x, y, z, and : R R is written as [x(u)] g(u)= y(u) [z(u)] Then the composition fois a function of just u. Use the chain rule to come up with an expression for of du Recall that, in terms of total derivatives, the chain rule says roughly that D( o ) = D D or, as matrices [D(f' og)] = [Df] [Dg] Or, to be more precise, using matrices, it says the following: [D('9)]|z, = [D]|g20) [Dg] | do