Math Solutions

(Steps Shown) If f(x,y,z)=x^2y-xz+y^3z , and x(r,s)=r+s^2,y(r,s)=rs,z(r,s)=2r-3s , use the chain rule to find the partial derivative with respect to s at

Question: If \(f\left( x,y,z \right)={{x}^{2}}y-xz+{{y}^{3}}z\) , and \(x\left( r,s \right)=r+{{s}^{2}},y\left( r,s \right)=rs,z\left( r,s \right)=2r-3s\) , use the chain rule to find the partial derivative with respect to s at r = 3, s = 5.

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