Expert: Paul Klarreich - 10/29/2005

Question
find the derivative of y with respect to x, t, or theta, as appropriate.

1) y=(x^2-2x+2)e^x
2) y=ln(3(theta)e^-theta

Answer
Hi, Amy,
Your basic rule:

D(e^x) = e^x, which I will usually write as exp(x)

combines with all the others, such as product, quotient, chain, etc.  So your examples are done this way:

1) y = (x^2 - 2x + 2)exp(x)  is a product rule example, in which the first function is  x^2 - 2x + 2 and the second function is exp(x)

I am afraid I cannot do your second example.  You have omitted a parenthesis, and its location is critical.

Keep in mind, of course:

A. The derivative of  ln(x) is 1/x

B. The ln and exp functions are inverses.  That means both:

   ln(exp(x)) = x
   exp(ln(x)) = x