Question

Z=2x^3y^5 полный Деферинциал

Answer 1

$z=2x^3y^5\\\\dz=z'_{x}\, dx+z'_{y}\, dy\\\\dz=6x^2y^5\, dx+10x^3y^4\, dy$

Answer 2

To find the total differential of the function Z = 2x^3y^5, we need to calculate the partial derivatives with respect to each variable and multiply them by the corresponding differentials. The total differential can be expressed as:

dZ = (∂Z/∂x)dx + (∂Z/∂y)dy

Let's calculate the partial derivatives:

∂Z/∂x = 6x^2y^5 ∂Z/∂y = 10x^3y^4

Now we can substitute these values back into the total differential equation:

dZ = (6x^2y^5)dx + (10x^3y^4)dy

So, the total differential of the function Z = 2x^3y^5 is given by:

dZ = (6x^2y^5)dx + (10x^3y^4)dy