Taking Velocity Derivative wrt X

Question

I was looking at some examples in my Fluid Mechanics textbook, and it showed that $$\frac{du(x)}{dx} = \frac{d}{dx}(v_0 + v_0\frac{R^3}{x^3}) = -3\frac{v_0^2}{R}\frac{1+(x/R)^3}{(x/R)^4} $$ where $v_0$ is the initial velocity of the fluid and $R$ is the radius of a sphere where the fluid traverses across. Both constants. When I tried to derive it by myself, I got the following: $$\frac{du}{dx} = -3v_0\frac{R^3}{x^4} $$ I do not understand how to reach the form that the book reaches, please help.

Answer 1

If $v_0$ and $R$ are constants, your book cannot be correct. One can easily check that without writing out the calculations.

You need more information on those parameters. Perhaps, you can read more context around that formula.