Question

大学高数高阶偏导数，求大神讲解，要详细过程？

Answer 1

z=5x^4+10x^2.y^3
∂z/∂x =20x^3+20xy^3
∂^2z/∂x^2 =60x^2+20y^3
∂z/∂y =30x^2.y^2

∂^2z/∂y^2 =60x^2.y
∂^2z/∂x∂y
=∂/∂x ( ∂z/∂y)
=∂/∂x ( 30x^2.y^2 )
=60x.y^2