Suppose that u = x²y, where x = r cos 0 and y = r sin 0. du Compute the partial derivatives du and дө using the chain rule. ar

Use the Chain Rule to find the indicated partial derivatives. z = x²+x²y, x=s+ 2t -u, y = stu²; az əz əz au when s= 4, t = 3, u = 1 as at az as az at az au 11 11 =

Find all the second order partial derivatives for f(r, y) = sin(2x) – a²e" + y?. Verify that the conclusion of Clairut's Theorem holds, that is fry = fyz.

Find ∂x/∂u and ∂y/∂u if the equations u = x2 - y2 and y = x2 - y define x and y as functions of the independent variables u and y, and the partial derivatives exist. Then let s = x2 + y2 and find ∂s/∂u.