Question

If u= x2 +y2 +z2 then prove that x du/dx + y du/dy + z du/dz =24

Answer 1

Answer:

Step-by-step explanation:

4x^2y^2 this is solve by derivative of u w.r.t x and y

Answer 2

Answer:

It can be solved by differentiating LHS separately and then adding them.

Step-by-step explanation:

It is given that $u=x^{2}+y^{2} +z^{2}$

We need to prove that

$x\frac{du}{dx} +y\frac{du}{dy}+z\frac{du}{dz} =2u$

Taking LHS

$x\frac{du}{dx} =2x^{2}$

Similarly $y\frac{du}{dy} =2y^{2}$

and

$z\frac{du}{dz} =2z^{2}$

Adding above three equations, we get

$x\frac{du}{dx} +y\frac{du}{dy}+z\frac{du}{dz} =2(x^{2} +y^{2} +z^{2} )$

As $x^{2} +y^{2} +z^{2} =u$

We get

$x\frac{du}{dx} +y\frac{du}{dy}+z\frac{du}{dz} =2u$

Hence, proved.

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