1. The problem statement, all variables and given/known data I have a question. How in general would one differentiate a composite function like F(x,y,z)=2x^2-yz+xz^2 where x=2sint , y=t^2-t+1 , and z = 3e^-1 ? I want to find the value of dF/dt evaluated at t=0 and I don't know how. Can someone please walk me through this? 2. Relevant equations Mod note: Fixed the equation below to match the OP's change above. F(x,y,z)=2x^2-yz+xz^2 dF/dx=4x-z^2 , dF/dy= -z , dF/dz = 2xz-y , dz/dt=0 , dx/dt=2cost, dy/dt=2t-1 dF/dx dx/dt + dF/dy dy/dt + dF/dz dz/dt= dF/dt 3. The attempt at a solution I tried a couple of things, including chain rules and jacobians. I know that dF/dt should equal dF/dx dx/dt + dF/dy dy/dt + dF/dz dz/dt but for some reason this doesn't work, or I am doing something wrong. I start out by differentiating to get dF/dx=4x-z^2 , dF/dy= -z , dF/dz = 2xz-y , dz/dt=0 , dx/dt=2cost, dy/dt=2t-1 but this doesn't match the answer, which my book says is 24. How do they get this, and where is my error? Thanks.