Question

Calculate the second-order partial derivatives. f (x, y) = 5 x^3 + 3 x^2 y + 4 xy^2 a) fxy = fyx = 30 x + 6 y, fxx = 8 x, fyy = 6 x + 8 y b) fxy = fyx = 6 x + 8 y, fxx = 6 x + 8 y, fyy = 6 x + 8 y c) fxy = fyx = 8 x, fxx = 6 x + 8 y, fyy = 3 x^2 + 8 xy d) fxy = fyx = 8 x, fxx = 30 x + 6 y, fyy = 30 x + 6 y e) fxy = fyx = 6 x + 8 y, fxx = 30 x + 6 y, fyy = 8 x f) None of these.

          Calculate the second-order partial derivatives.
f (x, y) = 5 x^3 + 3 x^2 y + 4 xy^2
a) fxy = fyx = 30 x + 6 y, fxx = 8 x,
fyy = 6 x + 8 y
b) fxy = fyx = 6 x + 8 y, fxx = 6 x + 8 y,
fyy = 6 x + 8 y
c) fxy = fyx = 8 x, fxx = 6 x + 8 y,
fyy = 3 x^2 + 8 xy
d) fxy = fyx = 8 x, fxx = 30 x + 6 y,
fyy = 30 x + 6 y
e) fxy = fyx = 6 x + 8 y, fxx = 30 x + 6 y,
fyy = 8 x
f) None of these.

Calculate the second-order partial derivatives.
f (x, y) = 5 x^3 + 3 x^2 y + 4 xy^2
a) fxy = fyx = 30 x + 6 y, fxx = 8 x,
fyy = 6 x + 8 y
b) fxy = fyx = 6 x + 8 y, fxx = 6 x + 8 y,
fyy = 6 x + 8 y
c) fxy = fyx = 8 x, fxx = 6 x + 8 y,
fyy = 3 x^2 + 8 xy
d) fxy = fyx = 8 x, fxx = 30 x + 6 y,
fyy = 30 x + 6 y
e) fxy = fyx = 6 x + 8 y, fxx = 30 x + 6 y,
fyy = 8 x
f) None of these.

Added by Nicole P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

03/16/2023

Step 1

First, we find the first-order partial derivatives: $$ f_x = \frac{\partial f}{\partial x} = 5 + 6xy + 4y $$ $$ f_y = \frac{\partial f}{\partial y} = 3x^2 + 4x $$ Now, we find the second-order partial derivatives: $$ f_{xx} = \frac{\partial^2 f}{\partial x^2} = Show more…

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Calculate the second-order partial derivatives. f(x, y) = 5 x^3 + 3 x^2 y + 4 xy^2 a) fxy = fyx = 30 x + 6 y, fxx = 8 x, fyy = 6 x + 8 y b) fxy = fyx = 6 x + 8 y, fxx = 6 x + 8 y, fyy = 6 x + 8 y c) fxy = fyx = 8 x, fxx = 6 x + 8 y, fyy = 3 x^2 + 8 xy d) fxy = fyx = 8 x, fxx = 30 x + 6 y, fyy = 30 x + 6 y e) fxy = fyx = 6 x + 8 y, fxx = 30 x + 6 y, fyy = 8 x f) None of these.