All Tasks

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

Chain rule arccotan

Applying the chain rule, calculate $\dfrac{dy}{dx}$ where $y=arccot(cos(x))$
 
# Functions of one variable

Training
13

Differential arccotan

Consider the function f defined by $f(x)=arccot(2x+1)$. Assuming $x=1$, what is the change in $x$ for which the change in $f$ is $0.3$? (enter the value with 1 decimal place)
 
# Functions of one variable

Reasoning
13

Differential at one point

Consider the function $f(x) = arccot \left(\dfrac{1}{x}\right),$ determine the differential of the function $f$ at the point of ordinate equal to $\dfrac{\pi}{4}$.
 
# Functions of one variable

Training
13

Differential of a function

Find the expression of $dy$ for the function $f(x) = arccot(3x)$.
 
# Functions of one variable

Training
13