How do you find the differential df given f(g,h) in terms of dg and dh
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How do you find the differential df given f(g,h) in terms of dg and dh

[From: ] [author: ] [Date: 11-06-22] [Hit: ]
f) h(g,i know how to find df/dg and df/dh using the chain rule,but I dont know how to find df in terms of dg and dh-If f = f(g,h),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.......
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

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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.
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