Chapter 3.1, Problem 8E

To compute the derivative of 2cosx with the chain rule by writing this function as a composition f(g(x)), what is the “outer” function f(x)? Explain your answers clearly.Then compute the derivative of the function.

Consider the function 2х + 1 g(x) = x +1 a) Evaluate the derivative of the function. b) Sketch the graph of the function, locating the x- and y- intercepts and all asymptotes.

In Exercises 1-4, use the definition f'(a) = lim la + h) – f(a) h to find the derivative of the given function at the indicated 1. f(x) = 1/x, a = 2 2. f(x) = x? + 4, a = 1 3. f(x) = 3 – x2, a = -1 In Exercises 5-8, use the definition 4. f(x) = x3 + x, a = 0 %3D f(x) – f(a} x - a f'(a) = lim to find the derivative of the given function at the indicated 5. f(x) = 1/x, a = 2 6. f(x) = x2 + 4, a = 1 %3D 7. f(x) = Vx + 1, a = 3 8. f(x) = 2x + 3, a = -1