suppose g is a function of h and f, and h is a function of g and f
[ that is g(h,f) h(g,f) ]
i know how to find df/dg and df/dh using the chain rule,
but I don't know how to find df in terms of dg and dh
[ that is g(h,f) h(g,f) ]
i know how to find df/dg and df/dh using the chain rule,
but I don't know how to find df in terms of dg and dh
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If f = f(g,h), then the total differential of f is given by:
df = [(∂f/∂g)_h]*dg + [(∂f/∂h)_g]*dh
where (∂f/∂g)_h is the partial derivative of f with respect to g at constant h, and (∂f/∂h)_g is the partial derivative of f with respect to h at constant g.
df = [(∂f/∂g)_h]*dg + [(∂f/∂h)_g]*dh
where (∂f/∂g)_h is the partial derivative of f with respect to g at constant h, and (∂f/∂h)_g is the partial derivative of f with respect to h at constant g.