#### Normal line of arccotan

Consider the function defined by $f(x)=4 arccot(x+1)$. Let $n$ be the normal line of $f$ for $x=0$ and let $A(-2\pi, k)$ one point of line $n$. Determine $k$.

# Functions of one variable

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#### Derivation arccotan

Consider $f(x)= 3arccot\left(2x-1\right)$ with domain $D_f=\mathbb{R}$. Let $f^{\prime}(x)$ be the first derivative of function $f(x)$, then $f^{\prime}\left(-\dfrac{1}{2}\right)$ is:

# Complements of differential calculus in real numbers

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#### Derivatives using arccotan

The derivative of the function $f(x)=2\text{arccot}(x+1)$ is:

# Functions of one variable

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#### Derivation arccotan

Let $\displaystyle f(x)= \pi -\dfrac{b}{3}arccot(2x)$ with $b \in \mathbb{R}$, and let $f^{\prime}(x)$ and $f^{\prime\prime}(x)$ be the first and the second derivative of the function $f$. Knowing that $\displaystyle f\left(\dfrac{\sqrt{3}}{2}\right) \cdot \dfrac{\sqrt{3} f^{\prime}\left(\dfrac{\sqrt{3}}{2}\right)}{2f^{\prime\prime}\left(\frac{\sqrt{3}}{2}\right)} = \dfrac{\pi}{4}$, then the value of $b$ is:

# Complements of differential calculus in real numbers

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#### Derivation arccotan

Let $f$ and $g$ be two differentiable functions in their domain, such that: $f(x)= \dfrac{\pi}{2} -\dfrac{1}{3}arccot(2x-1)$ and $g(x)=\left( x^2+x+2\right) f(x)$. Considering that $g^{\prime}(x)$ is the first derivative of function $g(x)$, then $g^{\prime}\left(0\right)$ is:

# Complements of differential calculus in real numbers

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#### Trigonometric equation

Solve the following trigonometric equation: $3arccot(x − \sqrt{3})− \pi=0$

# Functions of one variable

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