Some problems provide the opportunity for more than one mistake.

The Goal

Find

The Mistakes

Find the mistakes:

1.

Need a hint? Look carefully at the red part:

2.

Need a hint? Look carefully at the red part:

A Correct Solution

Explanations

In the first mistake the quotient rule was not used correctly. The quotient rule is:

In the mistake the numerator was taken to be just f'(z) - g'(z). Oops!

In the second mistake parentheses were not used around the g(z) part of the expression in the numerator, with the result that only the first part of g(z) was multiplied by f'(z). Use parentheses!