Finding derivatives?

Question

Basically, I have no idea how to do the following problems.

1. f(x) = ln(e^-x - x)
2. f(x) = (x^2 + 5)^3 (3x^3 - 2)^2
3. f(x) = (5x^2 + 11)e^-21x
4. y = (x^2 + √x + 1 ) / x^3/2

Any help would be appreciated; thanks in advance!

Answer 1

You can do each of those with a combination of the following:

The rules for taking the derivatives of a sum, difference, product, or quotient of two functions.

The Chain Rule.

Memorizing the derivatives of f(x) = x^n, n a constant (nx^(x-1), whether or not n is an integer) and e^x (just e^x).

It speeds things up if you also memorize that the derivative of e^(nx) is ne^(nx).