Consider a function f(x, y, z) given by

f(x, y, z) = $(x^{2} + y^{2} - 2 z^{2}) (y^{2} + z^{2})$

The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is
40

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Solution

The correct option is A 40
f(x, y, z) = $(x^{2} + y^{2} - 2 z^{2}) (y^{2} + z^{2})$

$f (x, y, z) = x^{2} y^{2} + y^{4} - 2 y^{2} z^{2} + x^{2} z^{2} + y^{2} z^{2} - 2 z^{4}$

$\frac{\partial f}{\partial x} = 2 x y^{2} + 0 - 0 + 2 x z^{2} + 0 - 0$
At x = 2, y = 1 and z = 3:
$\frac{\partial f}{\partial x} = 2 (2) (1)^{2}$ +2(2)(3) $^{2}$

= 4 +36 = 40

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