Derivatives + Integrals

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This is all the derivatives and integrals you should memorize for BC

34 Terms

1

Chain Rule

(d/dx) f(g(x)) = f’(g(x)) ⋅ g’(x)

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2

Product Rule

(d/dx) (f ⋅ g) = (f ⋅ g’) + (f’ ⋅ g)

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3

Quotient Rule

(d/dx) (f/g) = ((g ⋅ f’) - (f ⋅ g’))/g²

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4

Differentiation

The process of finding the derivative of a function, which measures how a function changes as its input changes.

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5
<p>⋅</p>

nu^(n-1) du/dx

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6
<p>⋅</p>

e^u du/dx

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7
<p>⋅</p>

a^u ⋅ ln(a) du/dx

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8
<p>⋅</p>

1/u du/dx

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9
<p>⋅</p>

1/(u⋅ln(b)) du/dx

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10
<p>⋅</p>

cos(u) du/dx

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11
<p>⋅</p>

-sin(u) du/dx

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12
<p>⋅</p>

sec²u du/dx

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13
<p>⋅</p>

-csc²(u) du/dx

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14
<p>⋅</p>

sec(u)tan(u) du/dx

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15
<p>⋅</p>

cot(u)csc(u) du/dx

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16
<p>⋅</p>

1/(sqrt(1-u²)) du/dx

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17
<p>⋅</p>

1/(1+u²) du/dx

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18
<p>⋅</p>

1/((u)(sqrt(1-u²))) du/dx

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19
<p>⋅</p>

1/(n+1) ⋅ u^(n+1) + C

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20
<p>⋅</p>

e^u + c

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21
<p>⋅</p>

(a^u)/(ln(a)) + C

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22
<p>⋅</p>

ln|u| + C

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23
<p>⋅</p>

(1/a) ⋅ ln|au+b| + C

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24
<p>⋅</p>

sin(u) + C

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25
<p>⋅</p>

-cos(u) + C

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26
<p>⋅</p>

tan(u) + C

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27
<p>⋅</p>

-cot(u) + C

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28
<p>⋅</p>

sec(u) + C

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29
<p>⋅</p>

-csc(u) + C

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30
<p>⋅</p>

arcsin(u) + C

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31
<p>⋅</p>

arctan(u) + C

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32
<p>⋅</p>

arcsec(u) + C

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33

What does LIPET stand for?

Logarithms, Inverse Trig, Polynomials, Exponents, Trig

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34

How do you do integration by parts?

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