1. The problem statement, all variables and given/known data The question asks to calculate ∂f/∂x for f(x,y,t) = 3x2 + 2xy + y1/2t -5xt where x(t) = t3 and y(t) = 2t5 2. Relevant equations The answer is given as ∂f/∂x = 6x + 2y - 5t 3. The attempt at a solution I'm confused because the answer given seems to treat x,y ,t as independent variables and the answer given is just a partial derivative treating y and t as constant. But really x,y.t are all dependent on each other. Is it even possible to obtain a partial derivative with respect to x in this case ?