Calculating Differential – Exercise 4231

Exercise

Find the differential of the function

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

Final Answer

Show 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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