Observe the graphs :

The function going from  towards , the slope of the tangent line to  increases and it approaches to  when approaches to .

In this region, the slope of the tangent line is always positive.

On the other hand, the function going from  towards , the negative slope of the tangent line to  increases and it approaches to  when  approaches to .

In this region, the slope of the tangent line is always negative.

Therefore, the function is  and its derivative function is .

Hence derivative of the function is  is suitable of the graph (c).

Graph (c) is the correct choice.