Find the function f'(x) that represents instantaneous rate of change, for each of the following below:

Question

Find the function f'(x) that represents instantaneous rate of change, for each of the following below:

a) f(x) = x^-2

f'(x) = ?

b) f(x) = 5x³

f'(x) = ?

c) f(x) = sqrt(x³)

f'(x) = ?

Answer 1

Hi Rocher!

Just wanted to quickly expand on Michael's answer with some explanations:

For a & b, we use the polynomial rule: the derivative of a function of the form a*x^b = ab*x^b-1.

For c, we're also using the polynomial rule - sqrt(x³) = x^3/2.

If you want to understand the derivations of those rules, I'd be happy to schedule a session with you - but for most calculus classes, it's sufficient to just memorize them.

Answer 2

a) f(x) = x^-2

f'(x) = -2x^-3

b) f(x) = 5x³

f'(x) = 15x²

c) f(x) = sqrt(x³)

f'(x) = (3/2)x^1/2