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.

a. Find the instantaneous growth rate of the population, for t≥0.

p(t) = 600 (t²+3/t²+9)

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)

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

f(x) = 1/x

Given that f(1) = 5, f′(1) = 4, g(1) = 2, and g′(1) = 3 , find d/dx (f(x)g(x))∣ ∣x=1 and d/dx (f(x) / g(x)) ∣ x=1.

Find the slope of the line tangent to the graph of f(x) = x / x+6 at the point (3, 1/3) and at (-2, -1/2).

Derivatives Find and simplify the derivative of the following functions.

f(x) = x /x+1