Find the derivative guys pls help

Question 1

Question 2

$\qquad\longrightarrow \sf f(x) = sin^(-1) \bigg((x)/(2)\bigg)\\$

The Derivative of f(x) with respect to x-

$\qquad\longrightarrow \sf (d)/(dx) \:sin^(-1) \bigg((x)/(2)\bigg)\\$

$\qquad\longrightarrow \sf \frac{1}{\sqrt{1-\bigg((x)/(2)\bigg)^2}}\;* (d)/(dx)\:(x)/(2)\\$

$\qquad\sf\because\boxed{\sf{ \: (d)/(dx) sin^(-1)x = (1)/(√(1-x^2))}}\\$

$\qquad\longrightarrow \sf \frac{1}{\sqrt{1-\bigg((x^2)/(4)\bigg)}}\;*(1)/(2) \:x^(1-1)\\$

$\qquad \sf\because\boxed{\sf{ (d)/(dx )x^n = nx^(n-1)}}\\$

$\qquad\longrightarrow \sf \frac{1}{\sqrt{1-\bigg((x^2)/(4)\bigg)}}\;*(1)/(2) * 1\\$

$\qquad\longrightarrow \sf \frac{1}{\sqrt{1-\bigg((x^2)/(4)\bigg)}}\;*(1)/(2) \\$

$\qquad\longrightarrow \sf(1)/(2)\: \frac{1}{\sqrt{1-\bigg((x^2)/(4)\bigg)}}\\$

$\qquad\longrightarrow \underline{\sf\: \frac{1}{2\:\sqrt{1-\bigg((x^2)/(4)\bigg)}}}\\$

Henceforth, Option C) is the correct answer.

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