A curve has equation y = (12x^1/2)-x^3/2
y = 12x1/2 - x3/2
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) x1/2. So putting it together the final answer is dy/dx = 6x-1/2 -(3/2) x1/2
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