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First, recognise that the function is a fraction and recall the quotient rule.     y=u/v     dy/dx=(vu'-uv')/v², where u' and v' is the derivative...

dy/dx = -6(0.5)x^-1.5+2

         = -3x^-1.5+2

Notice the denominator can be factorised as the difference of two squares. The fraction can then be simplified by cancellation. The resulting fraction(s) can then be solved using the list of integrals in ...

Layout the problem in a more recognisable form such as (3 - sqrt(5))(3 - sqrt(5)). Notice that this looks a lot like a factorised quadratic equation, where <...