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