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

8 0

3 years ago

Hi can you help me in mate plis simplify the following algebraic expressions

mars1129 [50]

Answer:

$\frac{3 {x}^{2} }{ {y}^{2} {z}^{6} }$