Question

differentiate with respect to x​

Answer 1

Step-by-step explanation:

We have,

$y = \sin^{ - 1} \{ \sqrt{ \frac{1 - x}{2} } \}$

$\frac{dy}{dx} = \frac{1}{ \sqrt{1 - \frac{1 - x}{2} } } . \frac{ - 1}{4 \sqrt{ \frac{1 - x}{2} } }$

$\implies \frac{dy}{dx} = - \frac{ \sqrt{2} }{ \sqrt{1 + x}} . \frac{ \sqrt{2} }{4 \sqrt{1 - x} }$

$\implies \frac{dy}{dx} = - \frac{ 2}{ 4\sqrt{1 - {x}^{2} }}$

$\implies \frac{dy}{dx} = - \frac{ 1}{ 2\sqrt{1 - {x}^{2} }}$