Question

If $y={\sin }^{-1}\left(\frac{x}{2}\right)+{\cos }^{-1}\left(\frac{x}{2}\right)$, then the value of $\frac{dy}{dx}$is

• A. $1$
• B. $-1$
• C. $0$
• D. $2$

Answer 1

The correct option is C

$0$

Explanation for the correct option:

Finding the value of $\frac{dy}{dx}$:

$y={\sin }^{-1}\left(\frac{x}{2}\right)+{\cos }^{-1}\left(\frac{x}{2}\right)$

We know that:

${\mathbf{sin}}^{\mathbf{-}\mathbf{1}}\mathbf{}\mathbf{\theta }\mathbf{+}{\mathbf{cos}}^{\mathbf{-}\mathbf{1}}\mathbf{}\mathbf{\theta }\mathbf{=}\frac{\mathbf{\pi }}{\mathbf{2}}$

So, $y=\frac{\mathrm{\pi }}{2}$

Differentiating with respect to $x$ both sides:

$\frac{dy}{dx}=0$ [As derivative of constant is $0$]

Hence, Option (C) is the correct answer.