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If , then . Assertion (A): If , then . Reason (R): .
Assertion: If $y = \sin^{-1}(x\sqrt{x})$, then $\frac{dy}{dx} = \frac{3\sqrt{x}}{2\sqrt{1-x^3}}$.
Reason: $\frac{d}{dx}(\sin^{-1} x) = \frac{1}{\sqrt{1-x^2}}, |x| \le 1$.
Assertion (A): If $y = \sin^{-1}(x\sqrt{x})$, then $\frac{dy}{dx} = \frac{3\sqrt{x}}{2\sqrt{1-x^3}}$.
Reason (R): $\frac{d}{dx}(\sin^{-1} x) = \frac{1}{\sqrt{1-x^2}}, |x| \le 1$.
- (a)Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
- (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of A.
- (c)Assertion (A) is true, but Reason (R) is false.
- (d)Assertion (A) is false, but Reason (R) is true.
Answer
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From ISC 2025 Practice Mathematics, question 43.