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5.0(1)

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hint

1

d/dx (a^{u})^{ }

= a^{u} ⋅ ln(a) ⋅du

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2

d/dx log_{a}(u)

= [du] / [u ⋅ ln(a)]

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3

d/dx sin(u)

= cos(u) ⋅ du

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4

d/dx cos(u)

= -sin(u) ⋅ du

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5

d/dx tan(u)

= sec^{2}(u) ⋅ du

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6

d/dx cot(u)

= -csc^{2}(u) ⋅ du

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7

d/dx sec(u)

= sec(u) ⋅ tan(u) ⋅ du

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8

d/dx csc(u)

= -csc(u) ⋅ cot(u) ⋅ du

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9

d/dx arcsin(u)

= [du] / [√(1-u^{2})]

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10

d/dx arccos(u)

= -[du] / [√(1-u^{2})]

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11

d/dx arctan(u)

= [du] / [u^{2}+1]

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12

d/dx arccot(u)

= -[du] / [u^{2}+1]

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13

d/dx arcsec(u)

= [du] / [u√(u^{2}-1)]

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14

d/dx arccsc(u)

= -[du] / [u√(u^{2}-1)]

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15

if the trig function starts with co-,

the derivative is negative

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16

tan(u) is with

sec(u)

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17

cot(u) is with

csc(u)

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18

derivatives of tan(u) and cot(u) are always…

squared

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19

how many terms are in the derivative of sec(u) and csc(u)?

3 terms

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