# Derivatives

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f(x)g(x)= . .

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## Tags and Description

### 31 Terms

1

f(x)g(x)= . .

f’(x)g(x)+f(x)g’(x) (*Product Rule*)

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2

f(x)/g(x)= . . .

f’(x)g(x)-f(x)g’(x)/(g(x))² (*Quotient Rule*)

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3

d/dx[f(g(x))]= . . .

f’(g(x))g’(x) (*Chain Rule*)

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4

d/dx(cf/(x))= . . .

cf’(x)

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5

d/dx(x^n)= . . .

nx^n-1

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6

d/dx(f(x)__+__g(x))= . . .

f’(x)__+__g’(x)

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7

d/dx(c)= . . .

0

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8

d/dx(e^g(x))= . . .

g’(x)e^g(x)

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9

d/dx[ln(g(x))]= . . .

g’(x)/g(x)

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10

d/dx[sin(x)]= . . .

cos(x)

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11

d/dx[cos(x)]= . . .

-sin(x)

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12

d/dx[csc(x)] = . . .

-csc(x)cot(x)

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13

d/dx[sec(x)]= . . .

sec(x)tan(x)

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14

d/dx[tan(x)]= . . .

sec²(x)

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15

d/dx[cot(x)]= . . .

-csc²(x)

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16

d/dx[sin⁻¹(x)]= . . .

1/√1-x²

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17

d/dx[cos⁻¹(x)]= . . .

-1/√1-x²

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18

d/dx[csc⁻¹(x)]= . . .

-1/lxl√1-x²

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19

d/dx[sec⁻¹(x)]= . . .

1/lxl√1-x²

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20

d/dx[tan⁻¹(x)]= . . .

1/1+x²

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21

d/dx[cot⁻¹(x)]= . . .

-1/1+x²

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22

d/dx[a^x]= . . .

a^x(ln(a))

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23

d/dx[ln(x)]= . . .

1/x, x>0

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24

d/dx[lnlxl]= . . .

1/x, x~~=0~~

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25

d/dx[log[a](x)]= . . .

1/x(ln(a)), x>0

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26

d/dx[sinh(x)]= . . .

cosh(x)

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27

d/dx[cosh(x)]= . . .

sinh(x)

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28

d/dx[tanh(x)]= . . .

sech²(x)

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29

d/dx[csch(x)]= . . .

-csch(x)coth(x)

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30

d/dx[sech(x)]= . . .

-sech(x)tanh(x)

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31

d/dx[coth(x)]= . . .

-csch²(x)

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