1.
a) Use the Chain Rule to calculate the partial derivatives. Express the answer in terms of the independent variables.
∂f 
∂r 
∂f 
∂t 
; f(x, y, z) = xy + z^{2}, x = r + s − 2t, y = 6rt, z = s^{2}

=  

= 
b) Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the independent variables.
∂F 
∂y 
; F(u, v) = e^{u+v}, u = x^{5}, v = 2xy
∂F 
∂y 
=
c)
Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the independent variables.
∂f 
∂u 
; f(x, y) = x^{2} + y^{2}, x = e^{u+v}, y = 2u + 4v
∂f 
∂u 
=
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