Calculating Differential – Exercise 4236

Exercise

Find the differential of the function

$h=x^3y^2+1$

Final Answer

Show final answer

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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