APFIVE Chain Rule Differentiation Error
In an experiment involving angle measurements, a student was tasked with differentiating the function $$y=\arcsin(2*x)$$. The correct derivative is $$\frac{2}{\sqrt{1-4*x^2}}$$, but the student computed it as $$\frac{1}{\sqrt{1-4*x^2}}$$. What did the student do wrong?
| x | Computed Derivative | Correct Derivative |
|---|---|---|
| 0.1 | 1.005 | 2.005 |
| 0.2 | 1.020 | 2.040 |
A
They computed the derivative correctly for the outer function but then incorrectly simplified the radical.
B
They misapplied the quotient rule, which was unnecessary in this context.
C
They mistakenly squared the inner function instead of differentiating it.
D
They neglected to multiply by the derivative of the inner function 2, thus omitting the constant factor 2 from the chain rule.
Question Leaderboard
Not enough data yet to show leaderboard.