Asked by Sara
Find all of the first partial derivatives of f(x,y,z)=arctan y/xz
Answers
Answered by
Steve
Remember - treat the other variables like constants.
Since d/dx arctan(u) = u'/(1+u^2)
Fx = (-y/zx^2)/(1+ y^2/x^2z^2)
Fy = (1/xz)//(1+ y^2/x^2z^2)
Fz = -y/xz^2)/(1+ y^2/x^2z^2)
you can massage them a bit if you like.
Since d/dx arctan(u) = u'/(1+u^2)
Fx = (-y/zx^2)/(1+ y^2/x^2z^2)
Fy = (1/xz)//(1+ y^2/x^2z^2)
Fz = -y/xz^2)/(1+ y^2/x^2z^2)
you can massage them a bit if you like.
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