## All Tasks

#### Inverse function derivative theorem arcsin

Consider $y=f(x)= \dfrac{\pi}{2} -2 \arcsin(1-2x)$ with domain $D_f=\left]0, 1 \right[ $.
Applying the inverse function derivative theorem, the expression of $\dfrac{dx}{dy}$ is:

# Complements of differential calculus in real numbers

Training

13

#### Inverse function derivative theorem arcsin

Consider $y=f(x)= 2 \arcsin\left(\dfrac{x}{3}\right)$ with domain $D_f=\left]-3, 3 \right[ $.
Applying the inverse function derivative theorem, the expression of $\dfrac{dy}{dx}$ is:

# Complements of differential calculus in real numbers

Training

13

#### Inverse function derivative theorem arcsin

Consider $y=f(x)= \dfrac{\pi}{2} -2 \arcsin(1-2x)$ with domain $D_f=\left]0, 1 \right[ $.
Applying the inverse function derivative theorem, the expression of $\dfrac{dy}{dx}$ is:

# Complements of differential calculus in real numbers

Training

13

#### Derivatives using arccotan

The derivative of the function $f(x)=2^{\text{arccot}\left(\ln\left(\sqrt{x-1}\right)-\sqrt{3}\right)}$ at the value of $x$ that is solution of the equation $\text{arccot}(x-3)=\dfrac{3\pi}{4}$ is:

# Functions of one variable

Training

13

#### Construction of a pipeline

Two construction companies participate in the construction of a natural gas pipeline. The construction section of the second company was 60 km shorter than the construction section of the first company. How many kilometers of pipeline were laid by each company?

# Linear equations

Modeling

9

#### How expensive are the clothes?

Julian buys a pair of jeans and a sweatshirt. The jeans are 5 times more expensive than the sweatshirt. In total he pays 63 €. How much € does each item cost?

# Linear equations

Training

9