A curve has equation y = (12x^1/2)-x^3/2

y = 12x^1/2 - x^3/2
First take the 1/2 power and multiply by the integer in front of the x (so 12 x 1/2 = 6), then minus 1 from the power (1/2 - 1 = -1/2) and replace the power above the x with -1/2. So that makes the first part of the equation = 6x^-1/2
Next we do the same to the second part of the equation, we take the 3/2 power and multiply by the integer in front of the x (so -1 x 3/2 = -3/2), then minus 1 from the power (3/2 - 1 = 1/2). So that makes the second part of the equation = (-3/2) x^1/2. So putting it together the final answer is dy/dx = 6x^-1/2 -(3/2) x^1/2