Find all values of x for which the function y=(the square root of x)/(5x-2) is differentiable.
In order for to be differentiable, then and must be defined, or real.
For , the numerator confines anything inside the squareroot to be greater than or equal to zero: .
When the denominator equals to zero, we know the function becomes undefined. This occurs when
Thus our conditions are: , not equal to
Upon differentiating to , we can see that the same conditions for are required for to be defined.