Question

Найти d^2z/dxdy функции z= y^3 cos sqrt(x)

Answer 1

 

$z = y^3cos(sqrt{x})\\ frac{partial z}{partial y} = 3y^2cos(sqrt{x})\\ frac{partial^2 z}{partial y partial x}= -3y^2*(frac{1}{2sqrt{x}})*sin(sqrt{x}) = boxed{ -frac{3y^2sin(sqrt{x})}{2sqrt{x}} }$