Basic derivatives of tan
Interactive practice questions
Consider the graph of $y=\tan x$y=tanx.
Which of the following best describes the graph of $y=\tan x$y=tanx?
The graph increases and decreases periodically.
It is constantly decreasing.
It is constantly increasing.
Which of the following best describes the nature of the gradient of the curve?
Select all the correct options.
The gradient is always negative.
The gradient to the curve is never $0$0.
The gradient function has the same period as the curve itself.
The gradient increases more and more rapidly as the curve approaches the asymptotes.
The gradient is always positive.
The gradient to the curve is $0$0 every $\pi$π radians.
The tangent lines at the intercepts of the curve have been graphed as well.
Using the graph, write down the gradient to the curve at $x=0$x=0, $\pi$π, $2\pi$2π, $3\pi$3π, $\text{. . .}$. . .
Gradient $=$= $\editable{}$.
The gradient function of $y=\tan x$y=tanx is $y'$y′. Which of the following is the correct graph of $y'$y′ for each value of $x$x?
Which of the following is the equation of the gradient function $y'$y′?
$y'=\sec^2\left(x\right)$y′=sec2(x)
$y'=\sec x$y′=secx
$y'=\csc^2\left(x\right)$y′=csc2(x)
$y'=\csc x$y′=cscx
Differentiate $y=4\tan x$y=4tanx.
Differentiate $y=4\tan x-1$y=4tanx−1.
Differentiate $y=\tan3x$y=tan3x.