(d)/(dx)[arccos((x)/(2))]=? Choose 1 answer: (A) (1)/(sqrt(1-(x^(2))/(4))) (B) (-1)/(sqrt(1-(x^(2))/(4))) (c) (1)/(2sqrt(1-(x^(2))/(4))) (D) (-1)/(2sqrt(1-(x^(2))/(4)))

Write Function: First, let's write down the function we need to differentiate: arccos(x/2).Apply Chain Rule: Now, we use the chain rule. The derivative of arccos(u) with respect to u is -1/sqrt(1-u^2). Here, u = x/2.Differentiate u: Differentiate u = x/2 with respect to x to get du/dx = 1/2.Use Chain Rule: Now, apply the chain rule: (d)/(dx)arccos(u) = (d arccos(u))/(du) * (du)/(dx).Plug in Derivatives: Plug in the derivatives: (d)/(dx)arccos(x/2) = -1/sqrt(1-(x/2)^2) * 1/2.Simplify Expression: Simplify the expression: (d)/(dx)arccos(x/2) = -1/(2sqrt(1-x^2/4)).Final Derivative: So, the derivative of arccos(x/2) with respect to x is (-1)/(2sqrt(1-(x^(2))/(4))).

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(d)/(dx)[arccos((x)/(2))]=?
Choose 1 answer:
(A)
(1)/(sqrt(1-(x^(2))/(4)))
(B)
(-1)/(sqrt(1-(x^(2))/(4)))
(c)
(1)/(2sqrt(1-(x^(2))/(4)))
(D)
(-1)/(2sqrt(1-(x^(2))/(4)))

$\frac{d}{d x}\left[\arccos \left(\frac{x}{2}\right)\right]=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{\sqrt{1-\frac{x^{2}}{4}}}$ $\newline$ (B) $\frac{-1}{\sqrt{1-\frac{x^{2}}{4}}}$ $\newline$ (c) $\frac{1}{2 \sqrt{1-\frac{x^{2}}{4}}}$ $\newline$ (D) $\frac{-1}{2 \sqrt{1-\frac{x^{2}}{4}}}$

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\frac{d}{d x}\left[\arccos \left(\frac{x}{2}\right)\right]=?

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{\sqrt{1-\frac{x^{2}}{4}}}

\newline

(B)

\frac{-1}{\sqrt{1-\frac{x^{2}}{4}}}

\newline

(c)

\frac{1}{2 \sqrt{1-\frac{x^{2}}{4}}}

\newline

(D)

\frac{-1}{2 \sqrt{1-\frac{x^{2}}{4}}}

Write Function: First, let's write down the function we need to differentiate: $\arccos\left(\frac{x}{2}\right)$ .
Apply Chain Rule: Now, we use the chain rule. The derivative of $\arccos(u)$ with respect to $u$ is $-\frac{1}{\sqrt{1-u^2}}$ . Here, $u = \frac{x}{2}$ .
Differentiate $u$ : Differentiate $u = \frac{x}{2}$ with respect to $x$ to get $\frac{du}{dx} = \frac{1}{2}$ .
Use Chain Rule: Now, apply the chain rule: $(\frac{d}{dx})\text{arccos}(u) = \frac{d \text{arccos}(u)}{du} * \frac{du}{dx}$ .
Plug in Derivatives: Plug in the derivatives: (\frac{d}{dx})\arccos(\frac{x}{$2$}) = -\frac{$1$}{\sqrt{$1$-(\frac{x}{$2$})^$2$}} \times \frac{$1$}{$2$}\.
Simplify Expression: Simplify the expression: \((\frac{d}{dx})\arccos(\frac{x}{2}) = -\frac{1}{2\sqrt{1-\frac{x^2}{4}}}.
Final Derivative: So, the derivative of $\arccos\left(\frac{x}{2}\right)$ with respect to $x$ is $\frac{-1}{2\sqrt{1-\left(\frac{x^{2}}{4}\right)}}$ .