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Example 3

Find the partial derivatives of

f(x,y,z) = sin(x2y - z)

at the point (1,0, 0).

To find fx(x, y, z) we treat y and z as constants.

fx(x,y,z) = 2xy cos(x2y - z).

fy(x,y,z) = x2 cos(x2y - z).

fz(x,y,z) = -cos(x2y - z).

Thus

fx(1,0,0) = 2 · 1 · 0 cos(12·0 - 0) = 0.

fy(1,0,0) = 12 cos(12 · 0 - 0) = 1.

fz(1,0,0) = -cos(12 · 0 - 0) = -1.


Last Update: 2006-11-15