यदि u = log (x^3 + y^3 + z^3 - 3xyz) है,तो le | vedclass

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(D) दिया गया है $u = \log (x^3 + y^3 + z^3 - 3xyz)$.हम जानते हैं कि $x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)$.अतः,$u = \l

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$3$

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(D) दिया गया है $u = \log (x^3 + y^3 + z^3 - 3xyz)$.हम जानते हैं कि $x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)$.अतः,$u = \log(x + y + z) + \log(x^2 + y^2 + z^2 - xy - yz - zx)$.आंशिक अवकलन करने पर:$\frac{\partial u}{\partial x} = \frac{3x^2 - 3yz}{x^3 + y^3 + z^3 - 3xyz}$$\frac{\partial u}{\partial y} = \frac{3y^2 - 3zx}{x^3 + y^3 + z^3 - 3xyz}$$\frac{\partial u}{\partial z} = \frac{3z^2 - 3xy}{x^3 + y^3 + z^3 - 3xyz}$इन अवकलनों का योग करने पर:$\frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} + \frac{\partial u}{\partial z} = \frac{3(x^2 + y^2 + z^2 - xy - yz - zx)}{(x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)}$$= \frac{3}{x + y + z}$$(x + y + z)$ से गुणा करने पर:$(x + y + z) \left( \frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} + \frac{\partial u}{\partial z} \right) = 3$.

यदि $u = \log (x^3 + y^3 + z^3 - 3xyz)$ है,तो $\left( \frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} + \frac{\partial u}{\partial z} \right) (x + y + z) =$

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