Let w(s, t)=f(u(s, t),v(s, t)) where u(1,0)=−6,∂u∂s(1,0)=5,∂u∂1(1,0)=7 v(1,0)=−8,∂v∂s(1,0)=−8,∂v∂t(1,0)=6 ∂f∂u(−6,−8)=−1,∂f∂v(−6,−8)=2

From the given set of conditions, it's likely that you are asked to find the values of and at the point .

By the chain rule, the partial derivative with respect to is



and so at the point , we have




Similarly, the partial derivative with respect to would be found via

C