Find the first and second derivatives

Question

Answer 1

We are given

y = 6x^2 - 10x - 7x^-2

To find the first derivative, we use the Power Rule for differentiation which says

d/dx[x^n] = nx^(n-1)

Applying this rule once to get the first derivative:

y' = 12x - 10 + 14x^-3

Applying this rule again to get the second derivative:

y'' = 12 - 42x^-4

Answer 2

The first derivative equals 12x-10+14x^{-3}. The second derivative equals 12-42x^{-4}.