Question:medium

If $y = e^{a \sin^{-1} x}$, then $(1 - x^2) y_2 - x y_1 =$

Show Hint

For functions of the form $y = e^{a f(x)}$, squaring and cross-multiplying the first derivative helps to eliminate the radical term before doing the second derivative.

Updated On: May 31, 2026

$a^2 y$
$-a^2 y$
$a y$
$-a y$

Show Solution

The Correct Option is A

Solution and Explanation

Was this answer helpful?

Questions Asked in AP EAPCET exam

Let \[ f(x)=\int \frac{\sqrt{x}}{(1+x)^2}\,dx \quad (x\geq 0) \] Then \[ f(3)-f(1) \] is equal to:

AP EAPCET - 2026
Definite and indefinite integrals

View Solution

Gas is being pumped into a spherical balloon at the rate of $ 30 \, \text{ft}^3/\text{min} $. Then the rate at which the radius increases when it reaches the value $ 15 \, \text{ft} $ is:

AP EAPCET - 2026
Differentiation

View Solution

Let the function $ f(x) $ be defined as $ f(x) = \frac{x - |x|}{x} $, then:

AP EAPCET - 2026
Definite and indefinite integrals

View Solution

If the direction ratios of two lines are given by $ l + m + n = 0 $ and $ mn - 2ln + lm = 0 $, then the angle between the lines is:

AP EAPCET - 2026
3D Geometry

View Solution

If $y = e^{a \sin^{-1} x}$, then $(1 - x^2) y_2 - x y_1 =$

Show Hint

The Correct Option is A

Solution and Explanation

Top Questions on Continuity and differentiability

Questions Asked in AP EAPCET exam