Solution Found!
Solution: Chain Rule with one independent variable Use
Chapter 11, Problem 11E(choose chapter or problem)
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)
Questions & Answers
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)