## All Tasks

#### Equation inverse trigonometric and its derivatives

Find $x$ solution of the equation
$$\frac{5}{2}-f'\left(\frac{4}{5}\right)-\arcsin(\sqrt{2}x)=f\left(\frac{4}{5}\right)$$
where $f$ is the function given by $f(x)=\text{arccot}(3-5x)-\pi$

# Functions of one variable

Training

13

#### Domain & Range of Arcsine

The graph of arcsine function is plotted in the picture in the domain [-1, 1]. Take a look at it and mark the correct statements subsequently.

# Functions of one variable

Learning

13

#### Tangent line arccotan

Let $f$ be the function defined by $f(x) =2-arccot(2x)$. The slope of the tangent line to $f$ at the point with the ordinate equal to 2 is
(enter the slope value to 2 decimal places)

# Functions of one variable

# Complements of differential calculus in real numbers

Training

13

#### 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

Training

13

#### 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

Training

13

#### Derivatives using arccotan

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

# Functions of one variable

Training

13