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Calculating Differential – Exercise 4236

Exercise

Find the differential of the function

h=x^3y^2+1

Final Answer


dh=3x^2y^2dx+2yx^3dy

Solution

We will find the function differential with the differential formula

dh=h'_x dx+h'_y dy

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

h'_x(x,y)=3x^2y^2

h'_y(x,y)=2yx^3

Now, we put the derivatives in the formula and get

dh=h'_x dx+h'_y dy

dh=3x^2y^2dx+2yx^3dy

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