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Question

Question: Differentiate $v=\sqrt{\frac{2GM}{r}}$ r is variable....

Differentiate

v=2GMrv=\sqrt{\frac{2GM}{r}}

r is variable.

Answer

dv/dr = -1/2 * sqrt(2GM) / r^(3/2)

Explanation

Solution

Solution Explanation:
Express the function as

v=2GMr=2GM  r−12v=\sqrt{\frac{2GM}{r}}=\sqrt{2GM}\;r^{-\frac{1}{2}}

Differentiate with respect to rr using the power rule:

dvdr=2GM(−12)r−32=−122GMr32.\frac{dv}{dr}=\sqrt{2GM}\left(-\frac{1}{2}\right)r^{-\frac{3}{2}}=-\frac{1}{2}\frac{\sqrt{2GM}}{r^{\frac{3}{2}}}.

Answer:

dvdr=−122GMr3/2\frac{dv}{dr}=-\frac{1}{2}\frac{\sqrt{2GM}}{r^{3/2}}