f(x,y,z)=e^(x²)sin(yz)+ln(x²+y²+z²).
∂f/∂x=2xe^(x²)sin(yz)+2x/(x²+y²+z²).
∂f/∂y=ze^(x²)cos(yz)+2y/(x²+y²+z²).
∂f/∂z=ye^(x²)cos(yz)+2z/(x²+y²+z²).
∂²f/∂x²=2e^(x²)sin(yz)+4x²e^(x²)sin(yz)+2(-x²+y²+z²)/(x²+y²+z²)².
∂²f/∂y²=-z²e^(x²)sin(yz)+2(x²-y²+z²)/(x²+y²+z²)².
∂²f/∂z²=-y²e^(x²)sin(yz)+2(x²+y²-z²)/(x²+y²+z²)².
∂²f/∂x∂y=∂²f/∂y∂x=2xze^(x²)cos(yz)-4xy/(x²+y²+z²)².
∂²f/∂x∂z=∂²f/∂z∂x=2xye^(x²)cos(yz)-4xz/(x²+y²+z²)².
∂²f/∂y∂z=∂²f/∂z∂y=e^(x²)cos(yz)-yze^(x²)sin(yz)-4yz/(x²+y²+z²)².