Suppose f is a differentiable function of x and y, and g(r,s) = f(2r-s,s^2-4r). Calculate dg/dr at (1,2) and dg/ds at (1,2) given that f(1,2)=6, g(1,2)=3, df/dx(1,2)=2 and df/dy(1,2)=5.
Suppose f is a differentiable function of x and y, and g(r,s) = f(2r-s,s^2-4r). Calculate dg/dr at (1,2) and dg/ds at (1,2) given that f(1,2)=6, g(1,2)=3, df/dx(1,2)=2 and df/dy(1,2)=5.
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Put x = 2r - s, y = s^2 - 4r ==> g(r,s) = f(x(r,s),y(r,s)) ==>
dg/dr = (df/dx)(dx/dr) + (df/dy)(dy/dr) = (df/dx)*2 + (df/dy)*(-4), and since at (1,2) we have (df/dx)(1,2) = 2 and (df/dy)(1,2) = 5, we get....well, now you end the argument.