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Calculating Differential – Exercise 4229

Exercise

Find the differential of the function

z=x^2y^4-x^3y^3+x^4y^2

Final Answer


dz=(2xy^4-3x^2y^3+4x^3y^2) dx+(4y^3x^2-3y^2x^3+2yx^4)dy

Solution

We will find the function differential with the differential formula

dz=z'_x dx+z'_y dy

In the formula above we see the function partial derivatives. Hence, we calculate them.

z'_x(x,y)=2xy^4-3x^2y^3+4x^3y^2

z'_y(x,y)=4y^3x^2-3y^2x^3+2yx^4

Now, we put the derivatives in the formula and get

dz=z'_x dx+z'_y dy

dz=(2xy^4-3x^2y^3+4x^3y^2) dx+(4y^3x^2-3y^2x^3+2yx^4)dy

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