Chain Rule Derivatives

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25 Terms

1
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d/dx(cu)

cu’

2
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d/dx(u+-v)

u’+-v’

3
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d/dx(uv)

uv’+u’v

4
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d/dx(u/v)

(vu’ - uv’)/v²

5
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d/dx( c )

0

6
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d/dx(u^n)

nu^(n-1) • u’

7
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d/dx( x )

1

8
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d/dx(|u|)

(u/|u|) • u’

9
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d/dx(lnu)

(1/u) • u’

10
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d/dx(e^u)

e^u • u’

11
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d/dx(loga(u))

(1/uln(a)) • u’

12
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d/dx(a^u)

a^u • lna • u’

13
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d/dx(sinu)

cosu • I’

14
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d/dx(cosu)

-sinu • u’

15
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d/dx(tanu)

sec²u • u’

16
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d/dx(cscu)

-cscucotu • u’

17
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d/dx(secu)

secutanu • u’

18
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d/dx(cotu)

-csc²u • u’

19
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d/dx(arcsinu)

(u’/sqrt(1-u²)

20
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d/dx(arccosu)

-u’/sqrt(1-u²)

21
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d/dx(arctanu)

u’/1+u²

22
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d/dx(arccscu)

-u’/(|u| • sqrt(u²-1)

23
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d/dx(arcsecu)

u’/(|u| • sqrt(u²-1)

24
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d/dx(arccotu)

-u’/(|u| • (u²+1))

25
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