1. The problem statement, all variables and given/known data The equation is z= e (x*y), the interesting thing is y is function of x too, y = ψ(x) Calculate the partial derivative respect to x, and the total derivative. 2. Relevant equations Total differential: dz= ∂z/∂x dx + ∂z/∂y dy 3. The attempt at a solution Well, according to the book: ∂z/∂x= y * exy But I don't agree with this result, because if y is also function of x this term will be different. For example if y=x3, z would be = ex4, and the partial derivative is: ∂z/∂x = 4 x3 * e x4 and this is not the same as: y * e xy = x3ex4 What do you think? I just want to check if the book is right, this topic (multivariate differential calculus) is so important that I want to understand it correctly.