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 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!