## All Tasks

#### Chain rule arccos

Let $f$ be a diferentiable function in $\mathbb{R}$ and $g(x)=f(\arccos(2x-1))$. Find the derivative of $g$ at the point where the line $2x-2y=1$ intercepts the $x$ axis.

# Functions of one variable

Reasoning

13

#### Arcsin tangency point

Find the point of tangency at which the line $y-4x+1=0$ is tangent to the curve $y=\arcsin(4x-1)$

# Functions of one variable

Training

13

#### Tangent line of the arccos

Determine the equation of tangent line of $\arccos(x)$ for $x=0.6$.
The equation of the tangent line can be described by the function $t(x)=mx+b, m, b\in\mathbb{R}$.
Insert the values of $m$ and $b$ in the related check boxes. Round to two decimal digits each.

# Complements of differential calculus in real numbers

Training

13

#### 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