Question

Find the first derivative?

Answer 1

You could do the question the way it is  written, but it is far easier to bring the negative power up to the numerator.

y= x^2 - 3. The derivative of that is
dy/dx = 2x The three is a constant and is always dropped when a derivative is taken
d(-3)/dx = 0

If you are a purist and want to solve the question the way it is written, you could do it this way.

dy/dx = d(1)/dx x^-2 - d(x^-2)/dx * 1
             ======================                    
                          (x^-2)^2

dy/dx =  - (-2 x^ - 3) / x^-4

dy/dx = 2 x^-3 * x^4
dy/dx = 2 x^(-3 + 4)
dy/dx = 2x ^ 1
dy/dx = 2x <<<<< answer