Find the value of dy/dx at the point where x = 2 on the curve with equation y = x^ 2 √(5x – 1).

Here we must use the product rule to differeniate because x appears in both terms of the equation, therefore both parts must be differentiated. So we will set u= x² and v= (5x-1)^(1/2) written like this makes the power easy to see. du/dx=2x dv/dx=(1/2)(5)(5x-1)^(-1/2) Product rule dy/dx = udv/dx + vdu/dx dy/dx = (5/2)x²(5x-1)^(-1/2) + 2x(5x-1)^(1/2) Sub in the value of 2 dy/dx = (5/2)2²(5(2)-1)^(-1/2) + 2(2)(5(2)-1)^(1/2) dy/dx = 46/3 = 20/21/3 + 12 12 can be written as 36/3 so dy/dx= 10/3 + 36/3 = 46/3