Calculating Differential – Exercise 4242

Exercise

Find the differential of the function

$g=x^2y^4+xy^2-3x^2z+z^2y$

Final Answer

Show final answer

Solution

We will find the function differential with the differential formula

$dg=g'_x dx+g'_y dy+g'_z dz$

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

$g'_x(x,y,z)=2xy^4+y^2-6xz$

$g'_y(x,y,z)=4y^3x^2+2xy+z^2$

$g'_z(x,y,z)=-3x^2+2zy$

Now, we put the derivatives in the formula and get

$dg=g'_x dx+g'_y dy+g'_z dz$

$du=(2xy^4+y^2-6xz)dx+(4y^3x^2+2xy+z^2)dy+(-3x^2+2zy)dz$

Have a question? Found a mistake? – Write a comment below!
Was it helpful? You can buy me a cup of coffee here, which will make me very happy and will help me upload more solutions!