All Tasks
Differential Arctan
Consider the function $f(x)= -2 \arctan\left(2x\right)$ with domain $D_f = \mathbb{R}$.
The differential of the function $y=f(x)$ at the point $x=-\dfrac{1}{2}$ is:
# Complements of differential calculus in real numbers
Training
13
Approximate values arctan
Consider the function $f(x)= -2 \arctan\left(2x\right)$ with domain $D_f = \mathbb{R}$.
Using differentials, the approximate value of $\ -2 \arctan\left(0.02\right)$ is:
# Complements of differential calculus in real numbers
Training
13
Differential Arctan
Consider $f(x)= \dfrac{\pi}{2} -2 \arctan(1-2x)$ with domain $D_f=\mathbb{R} $.
Knowing that the value of $df(x_0)=4 \ dx$, the value of $x_0$, is:
# Complements of differential calculus in real numbers
Training
13
Arctan inverse function derivative theorem
Consider $y=f(x)= -2 \arctan\left(2x\right)$ with domain $D_f=\mathbb{R}$.
Applying the inverse function derivative theorem, the expression of $\dfrac{dx}{dy}$ is:
# Complements of differential calculus in real numbers
Training
13
Arctan inverse function derivative theorem
Consider $y=f(x)= -2 \arctan\left(2x\right)$ with domain $D_f=\mathbb{R}$.
Applying the inverse function derivative theorem, the expression of $\dfrac{dy}{dx}$ is:
# Complements of differential calculus in real numbers
Training
13
Arctan inverse function derivative theorem
Consider $y=f(x)= \dfrac{\pi}{2} -2 \arctan(1-2x)$ with domain $D_f=\mathbb{R}$.
Applying the inverse function derivative theorem, the expression of $\dfrac{dy}{dx}$ is:
# Complements of differential calculus in real numbers
Training
13