Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y), where x = r2 + s2 and y = 4rs, find ∂2z/(∂r ∂s). (Compare with this example.) ∂2z ∂r ∂s = ∂2z ∂x2 + ∂2z ∂y2 + ∂2z ∂x ∂y + ∂z ∂y

What's the difference between: x≥0 and nonnegative integer. ?

Find the gradient of f(x, y,z)equals=left parenthesis x squared plus y squared plus z squared right parenthesis superscript negative 1 divided by 2 baseline plus ln left parenthesis x right parenthesis x2+y2+z2−1/2+ln(xyz) at the point left parenthesis negative 2 comma 1 comma negative 2 right parenthesis(−2,1,−2).

Aclothing store has the sign shown in the shop window. pani sees the sign and wants to buy 3 shirts and 2 pairs of jeans. the cost of each shirt before the discount is $12, and the cost of each pair of jeans is $19 before the discount. write and simplify an expression to find the amount pani pays if a $3 discount is applied to her total