The problem asks to find the df/dt when f(x,y)=e^xy and x(t)= 1-t and y(t)= 1-t^

Question

The problem asks to find the df/dt when f(x,y)=e^xy and x(t)= 1-t and y(t)= 1-t^2. I know have to use the Chain Rule but I think I'm doing something wrong. I know the formula states df/dt= ?f/?x times dx/dt + ?f/?y times dy/dt. I think it's basically asking to take the partial derivative of f with respect to x and with respect to y, as well dx/dt and dy/dt. I know dx/dt should be = -1 and dy/dt should be = -2t, but I'm confused on how to take the partial derivitives and then to put all of this together to get df/dt. Thank you

Explanation / Answer

The partial derivative of f(x,y) with respect to the variable x means that you hold y as a constant, so you look at f(x,y) as a one-variable f(x) function and you derivative this function in the traditional way. because .

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