Math 100 midterm derivative rules

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14 Terms

1
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d/dx(x^n)

nx^n-1

2
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f(x)+g(x)

f’(x)g(x)+f(x)g’(x)

3
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f(x)/g(x)

f’(x)g(x)-f(x)g’(x)/(g(x))²

4
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f(g(x))

f’(g(x))g(x)

5
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a^x

a^xln(a)

6
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ln(x)

1/x

7
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log base(a) x

1/xln(a)

8
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sin(x)

cos(x)

9
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cos(x)

-sin(x)

10
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tan(x)

sec²(x)

11
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csc(x)

-csc(x)cot(x)

12
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sec(x)

sec(x)tan(x)

13
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cot(x)

-csc²(x)

14
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d/dx(1/f(x))

-f’(x)/f(x)²