Some problems provide the opportunity for more than one mistake.

The Goal

Find

The Mistakes

Find the mistakes:

1.

(Roll the mouse over the math to see a hint in red)

2.

(Roll the mouse over the math to see a hint in red)

A Correct Solution

(Roll the mouse over the area above to see the corrections in blue)

Explanations

In both mistakes the chain rule is not used correctly. The chain rule is:

In this example g(x) = 1 - e^x.

In the first mistake g'(x) was not computed, but instead g(x) was left in its place.

In the second mistake g'(x) was computed incorrectly; the minus sign in front of e^x in g(x) appears to have been ignored. Be careful with signs!