Differential equationsFind the indicated ∂ derivative.
3 months ago
Find the indicated ∂ derivative. f(x,y,z)=y/x+y+z; f_(y)(2,1,-1)
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Best Answer
cannedbeansss Staff answered 3 months ago
Given f(x,y,z)= (y)/(x+y+z) When differentiating with respect to y, assume x and z are constants, and use the Quotient Rule: ((u)/(v))' = (u'v-uv')/(v^(2)) to differentiate the function as a whole. f_(y)= (1(x+y+z)-y(1))/((x+y+z)^(2))= (x+z)/((x+y+z)^(2)) -> f_(y)(2,1,-1)= (2-1)/((2+1-1)^(2))= (1)/(4) Result: f_(y)(2,1,-1)= (1)/(4)
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