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Calculating Differential – Exercise 4231

Exercise

Find the differential of the function

u=x^2y+y^2z+x^2z

Final Answer


du=(2xy+2xz) dx+(x^2+2yz) dy+(y^2+x^2) dz

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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