Derivative + Antiderivative Rules

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Last updated 7:08 PM on 4/22/26
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15 Terms

1
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d/dx (a)

0

2
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d/dx (a u)

a du/dx

3
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d/dx (u+v)

du/dx + dv/dx

4
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d/dx u-v

du/dx - dv/dx

5
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d/dx (uv)

u dv/dx + v du/dx

6
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d/dx (u/v)

(v du/dx - u dv/dx)/v²

7
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d/dx (u^n)

n u^n-1 du/dx

8
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d/dx [f(u)]

f’(u) du/dx

9
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d/dx [ln u]

1/u du/dx

10
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d/dx (e^u)

e^u du/dx

11
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∫ k dx

kx + C

12
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∫ x^n dx

(x^n+1/n+1) + C

13
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∫ (f(x)+g(x)) dx

∫ f(x) dx + ∫ g(x) dx

14
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∫ 1/x dx

ln |x| + C

15
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∫ e^kx dx

1/k e^kx + C