Suppose distances are measured in lightyears and that the temperature T of a gaseous nebula is inversely proportional to the distance from a fixed point, which is the origin. The temperature 1 lightyear from the origin is 100 degrees celsius. Find the gradient of T at (x,y,z).(adsbygoogle = window.adsbygoogle || []).push({});

here's what I have:

[tex]d=\sqrt{x^2+y^2+z^2}=1[/tex]

[tex]d=x^2+y^2+z^2=1[/tex]

[tex]T=\frac{1}{x^2+y^2+z^2}[/tex]

so the gradient is:

[tex]T_x=-\frac{2x}{(x^2+y^2+z^2)^2}[/tex]

[tex]T_y=-\frac{2y}{(x^2+y^2+z^2)^2}[/tex]

[tex]T_z=-\frac{2z}{(x^2+y^2+z^2)^2}[/tex]

but this is not right, i where did I go wrong?

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# Finding the gradient

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