Derivatives Find and simplify the derivative of the following functions.

h(x) = (x−1)(2x²-1) / (x³-1)

Derivatives Find and simplify the derivative of the following functions.

g(w) = √w+w / √w-w

Derivatives Find and simplify the derivative of the following functions.

h(w) = w⁵/³ / w⁵/³+1

Derivatives Find and simplify the derivative of the following functions.

g(x) = x⁴/³-1 / x⁴/³+1

Population growth Consider the following population functions.

b. What is the instantaneous growth rate at t=5?

p(t) = 600 (t²+3/t²+9)

Population growth Consider the following population functions.

c. Estimate the time when the instantaneous growth rate is greatest.

p(t) = 600 (t²+3/t²+9)

Population growth Consider the following population functions.

e.Use a graphing utility to graph the population and its growth rate.

p(t) = 600 (t²+3/t²+9)

Higher-order derivatives Find f′(x),f′′(x), and f′′′(x).

f(x) = 1/x