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 this example when the chain rule is used to differentiate the square root expression, it must be used twice in succession. That's because this expression is the composite of a composite. In the both mistakes this compound chain rule computation is not performed correctly. The chain rule says that the derivative of f(g(h(t))) is:

In this example:

Here's an algebra challenge: simplify the answer given in "A Correct Solution". One result is: