AP CALC BC: Derivative Rules

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23 Terms

1
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power rule

d/dx x^n = nx^n-1

d/dx (cx^n) = c•nx^(n-1)

2
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product rule

d/dx (f(x) g(x)) = f(x)g'(x) + g(x) f'(x)

3
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quotient rule

d/dx (g(x) / h(x)) = (h(x) g'(x) - g(x) h'(x)) / h(x)^2

4
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d/dx (sinx)

cosx

5
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d/dx (cosx)

-sinx

6
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d/dx (tanx)

sec^2(x)

7
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d/dx (cscx)

-cscxcotx

8
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d/dx (secx)

secxtanx

9
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d/dx (cotx)

-csc^2(x)

10
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chain rule

d/dx f(g(x)) = f'(g(x)) • g'(x)

d/dx f(g(h(x))) = f'(g(h(x))) • g'(h(x)) • h'(x)

11
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d/dx(e^x)

e^x

12
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d/dx(e^u)

e^u(u')

13
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d/dx(b^x)

b^x • lnb

14
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d/dx(b^u)

b^u • lnb • u'

15
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d/dx(lnu)

1/u • u'

16
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d/dx(loga(x))

1 / (xlna)

17
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d/dx (loga(u))

1/(ulna) • u'

18
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d/dx (arcsin(x))

1/ √(1-x^2)

19
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d/dx (arccos(x))

-1/ √(1-x^2)

20
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d/dx (arctan(x))

1/(1 + x^2)

21
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d/dx (arccot(x))

- 1/(1 + x^2)

22
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d/dx (arcsec(x))

1/ (|x| • √x^2-1)

23
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d/dx (arccsc(x))

-1/ (|x| • √x^2-1)