Differential equationsFind the indicated partial derivative. f(x,y,z)=y/x+y+z; f_(y)(2,1,-1)
8 months ago
Find the indicated partial derivative. f(x,y,z)=y/x+y+z; f_(y)(2,1,-1)
1 Answers
Best Answer
Dmar6074 Staff answered 8 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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