Some problems provide the opportunity for more than one mistake.

The Goal

Find

Mistake 1

Find the mistake:

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

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

Mistake 2

Find the mistake:

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

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

Mistake 3

Find the mistake:

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

Correction 3

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

Explanations

In the first mistake the chain rule is not used correctly. The chain rule says:

In this example f(x) = sin^-1(x) and g(x)=x². The g'(x) = 2x part is missing from the mistake.

In the second mistake the derivative was computed as f'(x)g'(x).

In the third mistake the derivative of inverse sine is incorrect.