AP EAMCET · Maths · Differentiation
If \(\quad u=\log \left(x^3+y^3+z^3-3 x y z\right), \quad\) then \((x+y+z)\left(u_x+u_y+u_z\right)\) is equal to
- A \(0\)
- B \(x-y+z\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
Given, \(u=\log \left(x^3+y^3+z^3-3 x y z\right)\) \[ \begin{aligned} & u_x=\frac{d u}{d x}=\frac{3 x^2-3 y z}{\left(x^3+y^3+z^3-3 x y z\right)} \\ & u_y=\frac{d u}{d y}=\frac{3 y^2-3 x z}{x^3+y^3+z^3-3 x y z} \end{aligned} \] and…
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