Comprehensive Review of Derivative Rules for Trigonometric and Inverse Trigonometric Functions

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14 Terms

1
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the derivative of sin(x) is ______.

cos(x)

2
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the derivative of cos(x) is _______.

-sin(x)

<p>-sin(x)</p>
3
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the derivative of tan(x) is _______.

sec^2(x)

<p>sec^2(x)</p>
4
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the derivative of cot(x) is _______.

-csc^2(x)

<p>-csc^2(x)</p>
5
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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>
6
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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>
7
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the derivative of (f^-1) is _____.

1/(f prime of f inverse)

<p>1/(f prime of f inverse)</p>
8
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the derivative of sin(x) inverse is _______.

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

<p>1/square root of (1-x^2)</p>
9
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the derivative of cos(x) inverse is ________.

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

<p>-1/square root of (1-x^2)</p>
10
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the derivative of tan(x) inverse is _____.

1/1+x^2

<p>1/1+x^2</p>
11
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the derivative of cot(x) inverse is ________.

-1/1+x^2

<p>-1/1+x^2</p>
12
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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>
13
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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>
14
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The chain rule means you will have the inverse function, replacing "x" with "u", followed by _______.

multiplying by u prime.

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