Comprehensive Review of Derivative Rules for Trigonometric and Inverse Trigonometric Functions

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14 Terms

1

the derivative of sin(x) is ______.

cos(x)

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2

the derivative of cos(x) is _______.

-sin(x)

<p>-sin(x)</p>
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3

the derivative of tan(x) is _______.

sec^2(x)

<p>sec^2(x)</p>
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4

the derivative of cot(x) is _______.

-csc^2(x)

<p>-csc^2(x)</p>
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5

the derivative of sec(x) is _______.

sin(x)/cos^2(x) OR sec(x) * tan(x)

<p>sin(x)/cos^2(x) OR sec(x) * tan(x)</p>
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6

the derivative of csc(x) is ________.

-cos(x)/sin^2(x) OR -csc(x) * cot(x)

<p>-cos(x)/sin^2(x) OR -csc(x) * cot(x)</p>
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7

the derivative of (f^-1) is _____.

1/(f prime of f inverse)

<p>1/(f prime of f inverse)</p>
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8

the derivative of sin(x) inverse is _______.

1/square root of (1-x^2)

<p>1/square root of (1-x^2)</p>
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9

the derivative of cos(x) inverse is ________.

-1/square root of (1-x^2)

<p>-1/square root of (1-x^2)</p>
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10

the derivative of tan(x) inverse is _____.

1/1+x^2

<p>1/1+x^2</p>
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11

the derivative of cot(x) inverse is ________.

-1/1+x^2

<p>-1/1+x^2</p>
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12

the derivative of sec(x) inverse is ________.

1/absolute value of x times square root of (x^2-1)

<p>1/absolute value of x times square root of (x^2-1)</p>
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13

the derivative of csc(x) inverse is _______.

-1/absolute value of x times square root of (x^2-1)

<p>-1/absolute value of x times square root of (x^2-1)</p>
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14

The chain rule means you will have the inverse function, replacing "x" with "u", followed by _______.

multiplying by u prime.

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