All Tasks

Inverse function derivative theorem arccotan

Applying the inverse function derivative theorem, to calculate the derivative of the derivative $\displaystyle\frac{dy}{dx}$ of the function $y=\mbox{arccot}(x)$ we get:
 
# Functions of one variable

Training
13

Equations using arccotan

Find the abscissa of the intersection point ​​between the curves $y=-\dfrac{3\pi}{2}\text{arccot}\left(\dfrac{2x+1}{3}\right)$ and $y=\ln e^{-\frac{3\pi^2}{8}}$.
 
# Functions of one variable

Training
13

Domain and range of arcsin

The domain ($D_f$) and the range ($D'_f$) of function $f(x)= 2 \arcsin\left(\dfrac{x}{3}\right)$ are, respectively,
 
# Functions of one variable

Training
13

Domain and range of arcsin

The domain ($D_f$) and the range ($D'_f$) of function $f(x)= \dfrac{\pi}{2} -2 \arcsin(1-2x)$ are, respectively,
 
# Functions of one variable

Training
13

Inverse function derivative theorem arccotan

Let $g(x)=\mbox{arccot}(x)$. Applying the inverse function derivative theorem, the expression of $\left(g^{-1}\right)'(x)$, is:
 
# Functions of one variable

Training
13

Chain rule arccot

Applying the chain rule, calculate $\frac{dy}{dx}$ where $y=arccot(u^2+1)$, and $u=\sqrt{x+1}$.
 
# Functions of one variable

Training
13