Question

Calculate fxxyz if f(x,y,z) = sin(3x+yz) .

Answer 1

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Question #42375, Math, Integral Calculus

Calculate fxxyz if $f(x,y,z) = \sin(3x + yz)$.

Solution. $f(x, y, z) = \sin(3x + yz)$

$$f_x(x, y, z) = 3\cos(3x + yz)$$ $$f_{xx}(x, y, z) = -9\sin(3x + yz)$$ $$f_{xxy}(x, y, z) = -9z\cos(3x + yz)$$ $$f_{xxyz}(x, y, z) = -9\cos(3x + yz) + 9yz\sin(3x + yz).$$

Answer. $f_{xxyz}(x, y, z) = 9[yz\sin(3x + yz) - \cos(3x + yz)]$.