All Tasks

Chain rule arcsin

Let $f$ be a continuous function on $\mathbb{R}$ and $g$ the function $g(x)=\pi-\arcsin(3+2x)$. Knowing that $f\left(\pi\right)=0$ and $f'\left(\pi\right)=-1$, find the value of the derivative $\left(f\left(g\left(-\frac{3}{2}\right)\right)\right)'$.
 
# Functions of one variable

Training
13

Chain rule arcsin

Let $y=y(x)=\arcsin(2-3x)$ and $x=x(t)=e^{3t^2}$. Use the chain rule formula to express the derivative $\left.\frac{dy}{dt}\right|_{t=0}$.
 
# Functions of one variable

Training
13

terms square 1

The depicted sequence of matchstick figures is continued. Indicate the number of matchsticks at the 4th step.
 
# Terms with variables

Modeling
7

Perimeter triangle

In an isosceles triangle, the base is 5 cm longer than each leg. Set up a term that can be used to determine the perimeter of the figure.
 
# Terms with variables

Modeling
7

Sequence of triangles 2

Determine a term that can be used for each step to determine the number of small triangles from which each figure is built.
 
# Terms with variables

Modeling
8

Sequence of squares 2

Determine a term that can be used for each step to determine the number of small squares from which each figure is built.
 
# Terms with variables

Modeling
6