Help: critical numbers and logorithmic differentiation

[meshun01]

1.) The function f(x)= (4x + 8)e^-4x has one critical number. What is it?

9.) f(x) = x^2x
Use logorithmic differentiation to determine the derivative
f'(x) =
f'(1) =

 

[stapel]

1) What did you get for your derivative?

9) Is this "f(x) = x^2x"? If so, follow the usual procedure:

. . . . .f(x) = x^2x

. . . . .y = x^2x

. . . . .ln(y) = 2x ln(x)

Differentiate, solve for "(dy/dx)=", plug in "x^2x" for "y", and rename "dy/dx" as "f'(x)". Then evaluate at x = 1.

If you get stuck, please reply showing your steps.

Thank you.

Eliz.