Question

1. a) Use the Chain Rule to calculate the partial derivatives. Express the answer in terms...

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 + z2,    x = r + s − 2t,    y = 6rt,    z = s2

∂f
∂r
=
∂f
∂t
=

b) Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the independent variables.

∂F
∂y

;    F(u, v) = eu+v,    u = x5,    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) = x2 + y2,    x = eu+v,    y = 2u + 4v

∂f
∂u

=

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