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Find the total differential.
z = 2x3y9

1 Answer

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Answer:

dz = (6x^2y^9)dx + (18x^3y^8)dy.

Explanation:

To find the total differential of the function z = 2x^3y^9, we need to compute its partial derivatives with respect to x and y, and then express the total differential in terms of dx and dy.

Let's start by finding the partial derivative of z with respect to x, assuming y is constant:

∂z/∂x = ∂(2x^3y^9)/∂x

= 6x^2y^9

Next, let's find the partial derivative of z with respect to y, assuming x is constant:

∂z/∂y = ∂(2x^3y^9)/∂y

= 18x^3y^8

Now that we have the partial derivatives, we can express the total differential of z as:

dz = (∂z/∂x)dx + (∂z/∂y)dy

Substituting the partial derivatives we found earlier:

dz = (6x^2y^9)dx + (18x^3y^8)dy

So, the total differential of z = 2x^3y^9 is given by dz = (6x^2y^9)dx + (18x^3y^8)dy.

User Peter Davis
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