Find the first and second derivatives

Question

Answer 1

We are given

r = 1/3s^-2 - 5/4s^-3

The Power Rule for Differentiation will be used

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

Applying this rule once to find the first derivative

r' = -2/3s^-3 + 15/4s^-4

Applying this rule again to find the second derivative

r'' = 2s^-4 -15s^-5

Answer 2

Rewrite as:

r = (1/3)s^-2 -(5/4)s^-3 (then apply the power rule)

dr/ds = (-2/3)s^-3 +(15/4)s^-4

r'' = 2s^-4 - 15s^-5

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