If y = sin⁻¹(x√x), then (dy)/(dx) = (3√x)/(2√(1-x³)). Assertion (A): If y = sin⁻¹(x√x), then (dy)/(dx) = (3√x)/(2√(1-x³)). Reason (R): d/(dx)(sin⁻¹ x) =…

Answer: (c) Assertion (A) is true, but Reason (R) is false. Correct: (c)

Mathematics20251 markAssertion-reasonContinuity, Differentiability and Differentiation

Study the Assertion and Reason and choose the correct option.

If y = sin⁻¹(x√x), then (dy)/(dx) = (3√x)/(2√(1-x³)). Assertion (A): If y = sin⁻¹(x√x), then…

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

Official answer key

Correct option: (c)

Answer: (c) Assertion (A) is true, but Reason (R) is false.