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)

3.

(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 the first mistake the product rule is not used, and in addition the chain rule is not used to find the derivative of ln(bx). The same failure to use the chain rule occurs in the second mistake, while in the third mistake the chain rule is used incorrectly.

The chain rule is applied to the natural logarithm of a function g(x) as follows:

In this example g(x) = bx, so g'(x) = b.