Solution: Chain Rule with one independent variable Use

Chapter 11, Problem 11E

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QUESTION:

Chain Rule with one independent variable Use Theorem 12.7 to find the following derivatives. When feasible, express your answer in terms of the independent variable.

dw/dt, where w = xy sin z, \(x=t^{2}, y=4 t^{3}, \text { and } z=t+1)

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QUESTION:

Chain Rule with one independent variable Use Theorem 12.7 to find the following derivatives. When feasible, express your answer in terms of the independent variable.

dw/dt, where w = xy sin z, \(x=t^{2}, y=4 t^{3}, \text { and } z=t+1)

ANSWER:

Solution 11EStep 1 of 3:In this problem we need to find the derivative of w. That is , .Chain rule with one independent variable : Let w be a function of three variables (x , y,z) ,differentiable on an open domain ‘D’ .Suppose that x ,y and z are function of a single variable t differentiable on an open interval ‘’ and such that for every , .Then w(x(t),y(t),z(t)) is a function of t , differentiable on and we have : …………..(1)

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