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Hint

1

sinx

cosx

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2

cosx

-sinx

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3

tanx

sec²x

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4

cotx

-csc²x

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5

secx

secx*tanx

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6

cscx

-cscx*cotx

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7

arcsinx

1

√(1-x²)

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8

arccosx

-1

√(1-x²)

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9

arctanx

1

1+x²

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10

arccotx

-1

1+x²

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11

arcsecx

1

|x|√(x²-1)

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12

arccscx

-1

|x|√(x²-1)

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13

How are the arctrig derivatives related?

For each of the pairs of derivatives (arcsin/arccos, arctan/arccot, and arcsec/arccsc) the one that starts with co is negative and the one that does not is positive. Every other part of the equation is the same.

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14

How can you apply the chain rule to arctrig?

The derivative of the inside function goes in the numerator, while the derivative of the outside function goes in the denominator.

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