The point $P$ travels along the curve $C$ with equation $y = x \sin^{-1} x$, \(-1

Question

The point $P$ travels along the curve $C$ with equation $y = x \sin^{-1} x$, $-1 < x < 1$. Let the gradient of the curve $C$ at the point $P$ be $m$. If the $x$-coordinate of $P$ is increasing at the rate of $9$ units per second when $x = \frac{1}{2}$, find the exact value of the rate at which $m$ is changing at this instant.[4]

Accepted Answer

$14\sqrt3\text{ units per second}$.

2025 RI P1 Q2

2025 RI P1 Q2

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