Question

differentiation...
please help :)

Answer 1

\[\rm If~~\frac{ x^2 }{ 1+u }+\frac{ y^2 }{ 2+u }+\frac{ z^2 }{ 3+u }=1\]
then prove that : \(\rm u^2_x+u^2_y+u^2_z=2[x \cdot u_x+y \cdot u_y+z \cdot u_z]\)

Answer 2

can u please tell what are-\[u_{x} ,u_{y},u_{z}\]

Answer 3

partial derivative

Answer 4

oh ok :)

Answer 5

we can simplify it to this-
\[\rm u^2_x+u^2_y+u^2_z=2[x \cdot u_x+y \cdot u_y+z \cdot u_z]\]\[u_{x}^2-2xu_{x}+x^2+u_{y}^2-2yu_{y}+y^2+u_{z}^2-2zu_{z}+z^2=x^2+y^2+ z^2\]\[(u_{x}-x)^2+(u_{y}-y)^2+(u_{z}-z)^2=x^2+y^2+z^2\]
m still a lil confused with u_{x},u_{y} can u gimme a lil more idea
is u_{x] the partial derivative of the whole equation with respect to x?