Exercise
Find the differential of the function
u=x^2y+y^2z+x^2z
Final Answer
Solution
We will find the function differential with the differential formula
du=u'_x dx+u'_y dy+u'_z dz
In the formula above we see the function partial derivatives. Hence, we calculate them.
u'_x(x,y,z)=2xy+2xz
u'_y(x,y,z)=x^2+2yz
u'_z(x,y,z)=y^2+x^2
Now, we put the derivatives in the formula and get
du=u'_x dx+u'_y dy+u'_z dz
du=(2xy+2xz) dx+(x^2+2yz) dy+(y^2+x^2) dz
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