Mathematics, 19.10.2019 03:20 dejah791
If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j β k. solution (a) the gradient of f is βf(x, y, z) = fx(x, y, z), fy(x, y, z), fz(x, y, z) = . (b) at (2, 4, 0) we have βf(2, 4, 0) = < 0,0,8> . the unit vector in the direction of v = i + 3j β k is u = < 1 β11, 3 β11,β 1 β11> . therefore this equation gives duf(2, 4, 0) = βf(2, 4, 0) Β· u = 8k Β· 1 β11, 3 β11,β 1 β11 = β 8 β11 .
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If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f a...
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