Mathematics

The key is recognizing that you need the derivative formula for $\arcsin x$, not the value of $\arcsin$ itself. Once you have that formula, you'll substitute $x = \frac{3}{5}$ directly—but here's the insight: you'll need to simplify $\sqrt{1 - x^2}$ at that specific value, which involves recognizing a Pythagorean triple or basic algebra. The answer is a clean fraction.

The key is recognizing that you need the derivative formula for $\arcsin x$, not the value of $\arcsin$ itself. Once you have that formula, you'll substitute $x = \frac{3}{5}$ directly—but here's the insight: you'll need to simplify $\sqrt{1 - x^2}$ at that specific value, which involves recognizing a Pythagorean triple or basic algebra. The answer is a clean fraction.