A curve has the equation y = 4x^3 . Differentiate with respect to y.

y = 4x³ To differentiate you must find dy/dx. To calculate dy/dx, look at this example using just letters from algebra: y = ax^b dy/dx = (ab)x^(b-1) As you can see, to calculate dy/dx you must multiply the number preceding x (in this example this number is represented by the letter: a) by the number that x is to the power of (which is in this case is represented by the letter: b). You then subtract 1 from the integer to give you a new integer (in this case represented by: b-1). Using this logic, we will go through the question in a couple of steps. Firstly, identify which numbers represent 'a' and 'b' in this question: y = 4x³ So, a = 4, and b=3. Putting these numbers into our formula (dy/dx = (ab)x^(b-1) ) gives us: ab = 12 b - 1 = 2 Therefore, we can substitute these answers into our formula, giving us our final answer: dy/dx = 12x²