Question A2 (3 marks) Consider the function
f(x,y)=x^(3)+2xy+y^(2)sinx.
Find the partial derivatives
f_(x)
and
f_(y)
everywhere. Using your preferred differentiability test (e.g., checking the continuity of partial derivatives in a neighborhood), determine whether
f
is differentiable at
(0,0)
. State clearly any theorems or results used in your conclusion.

Question

Question A2 (3 marks) Consider the function

f(x,y)=x^(3)+2xy+y^(2)sinx.

Find the partial derivatives

f_(x)

and

f_(y)

everywhere. Using your preferred differentiability test (e.g., checking the continuity of partial derivatives in a neighborhood), determine whether

f

is differentiable at

(0,0)

. State clearly any theorems or results used in your conclusion.

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Solution for - Question A2 (3 marks) Consider the function f(x,y)=x^(3)+2xy+y^(2)sinx. Find the partial derivatives

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(Solved): Question A2 (3 marks) Consider the function f(x,y)=x^(3)+2xy+y^(2)sinx. Find the partial derivatives ...