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