Memorized Derivatives

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23 Terms

1
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d/dx(c)

0

2
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d/dx(cx)

c

3
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d/dx(rad(x))

1/(2rad(x))

4
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d/dx(|x|)

x/|x| or |x|/x

5
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d/dx(1/x)

-1/x²

6
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d/dx(x^n)

nx^n-1

7
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d/dx(sinx)

cosx

8
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d/dx(cosx)

-sinx

9
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d/dx(e^x)

e^x

10
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d/dx(lnx)

1/x

11
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d/dx(f(x)*g(x))

f(x)g’(x) + f ’(x)g(x)

12
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d/dx(f(x) / g(x))

(g(x)f ’(x) - f(x)g’(x)) / (g(x))²

13
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d/dx(tanx)

sec²x

14
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d/dx(cotx)

-csc²x

15
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d/dx(secx)

secxtanx

16
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d/dx(cscx)

-cscxcotx

17
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d/dx(f(g(x))

f ’(g(x))*g’(x)

18
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d/dx(a^f(x))

f ’(x)*ln(a)*(a^f(x))

19
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d/dx(arcsin(f(x))

f ’(x)/rad(1-(f(x))²)

20
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d/dx(arccos(f(x))

-f ’(x)/rad(1-(f(x))²)

21
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d/dx(arctan(f(x))

f ‘(x)/1+(f(x))²

22
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d/dx(logb(f(x))

f ‘(x)/f(x)*ln(b)

23
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If f(x) and g(x) are inverses:


d/dx(g(x))

g’(x) = 1/f ‘(g(x))