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Question
If
f(x)=arccos(x), then what is the value of
f^(')((sqrt3)/(2)) in simplest form?
Answer Attempt 1 out of 2
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Question $\newline$ If $f(x)=\arccos (x)$ , then what is the value of $f^{\prime}\left(\frac{\sqrt{3}}{2}\right)$ in simplest form? $\newline$ Answer Attempt $1$ out of $2$ $\newline$ Submit Answer

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Find derivatives of inverse trigonometric functions

Full solution

Q. Question

\newline

If

f(x)=\arccos (x)

, then what is the value of

f^{\prime}\left(\frac{\sqrt{3}}{2}\right)

in simplest form?

\newline

Answer Attempt

1

out of

2

\newline

Submit Answer

Derivative of arccos(x): step_1: What is the derivative of $f(x) = \text{arccos}(x)$ ? $\newline$ The derivative of $\text{arccos}(x)$ is $-\frac{1}{\sqrt{1-x^2}}$ . $\newline$ $\frac{d}{dx}(f(x)) = \frac{d}{dx}(\text{arccos}(x))$ $\newline$ $f'(x) = -\frac{1}{\sqrt{1-x^2}}$
Calculate $f'(\sqrt{3}/2)$ : step_2: Calculate the value of $f'(\sqrt{3}/2)$ . We substitute $x = \sqrt{3}/2$ into the derivative formula. $f'(\sqrt{3}/2) = -1/\sqrt{1-(\sqrt{3}/2)^2}$
Simplify expression: step_3: Simplify the expression under the square root. $\newline$ $1 - (\sqrt{3}/2)^2 = 1 - 3/4 = 1/4$
Calculate $f'(\sqrt{3}/2)$ : step_4: Calculate the value of $f'(\sqrt{3}/2)$ . $\newline$ $f'(\sqrt{3}/2) = -1/\sqrt{1/4}$ $\newline$ $f'(\sqrt{3}/2) = -1/(1/2)$ $\newline$ $f'(\sqrt{3}/2) = -2$

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