Mathematics - Calculus - Multivariable - Partial derivatives - Compute Partial Derivatives

10 problems: (1-2) f(x,y)=x³y²-2xy+y. Find ∂f/∂x and ∂f/∂y. (3-4) f(x,y)=eˣʸ. Find fₓ and f_y. (5-6) f(x,y)=sin(x²+y). Find both partials. (7) f(x,y,z)=xyz+x²z. Find ∂f/∂x, ∂f/∂y, ∂f/∂z. (8) Second partials: find fₓₓ, f_{yy}, f_{xy} for f=x²y³. (9) Gradient: find ∇f at point (1,2) for f=x²+xy. (10)