NZ Level 8 (NZC) Level 3 (NCEA) [In development]
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Basic derivatives of tan

Interactive practice questions

Consider the graph of $y=\tan x$y=tanx.

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a

Which of the following best describes the graph of $y=\tan x$y=tanx?

The graph increases and decreases periodically.

A

It is constantly decreasing.

B

It is constantly increasing.

C

The graph increases and decreases periodically.

A

It is constantly decreasing.

B

It is constantly increasing.

C
b

Which of the following best describes the nature of the gradient of the curve?

Select all the correct options.

The gradient is always negative.

A

The gradient to the curve is never $0$0.

B

The gradient function has the same period as the curve itself.

C

The gradient increases more and more rapidly as the curve approaches the asymptotes.

D

The gradient is always positive.

E

The gradient to the curve is $0$0 every $\pi$π radians.

F

The gradient is always negative.

A

The gradient to the curve is never $0$0.

B

The gradient function has the same period as the curve itself.

C

The gradient increases more and more rapidly as the curve approaches the asymptotes.

D

The gradient is always positive.

E

The gradient to the curve is $0$0 every $\pi$π radians.

F
c

The tangent lines at the intercepts of the curve have been graphed as well.

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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 $=$= $\editable{}$.

d

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?

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A

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B

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C

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D

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A

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B

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C

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D
e

Which of the following is the equation of the gradient function $y'$y?

$y'=\sec^2\left(x\right)$y=sec2(x)

A

$y'=\sec x$y=secx

B

$y'=\csc^2\left(x\right)$y=csc2(x)

C

$y'=\csc x$y=cscx

D

$y'=\sec^2\left(x\right)$y=sec2(x)

A

$y'=\sec x$y=secx

B

$y'=\csc^2\left(x\right)$y=csc2(x)

C

$y'=\csc x$y=cscx

D
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Differentiate $y=4\tan x$y=4tanx.

Differentiate $y=4\tan x-1$y=4tanx1.

Differentiate $y=\tan3x$y=tan3x.

Outcomes

M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

91578

Apply differentiation methods in solving problems

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