Exercise
Find the differential of the function
g=x^2y^4+xy^2-3x^2z+z^2y
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!