EXERCISE 8.6

EXERCISE . . If u x y x y e t and y = sin , find du dt and evaluate it at t = . . If u x y z xy z t y z du dt ( , , ) sin , cos , = + find . If w x y z z ( , , ) and z cos , find dw dt . . Let U x y z xyz x t z t t ( , , ) cos , sin ,  . Find dU dt . . If w x y s s s cos ,  , find dw ds , and evaluate at s = , . If z x y se tan ( ), s, −  . Find ∂ z s and ∂ z t at s = t = . . Let U x y , where x st s t s t  . Find ∂ U s U and evaluate them at s = t = . . Let z x y x y ( , ) = , where x se y se s t  . Find ∂ z s and ∂ z t . . W x y z yz zx x v y uv z v u v ( , , )  . Find W W v and evaluate them at ,   .