Dervative rules

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Last updated 9:08 PM on 10/5/26
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26 Terms

1
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Constant Rule

d/dx[c] = 0

<p>d/dx[c] = 0</p>
2
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Power Rule

d/dx[x^n] = n·x^(n−1)

<p>d/dx[x^n] = n·x^(n−1)</p>
3
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Constant Multiple Rule

d/dx[c·f(x)] = c·f′(x)

<p>d/dx[c·f(x)] = c·f′(x)</p>
4
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Sum Rule

d/dx[f(x) + g(x)] = f′(x) + g′(x)

<p>d/dx[f(x) + g(x)] = f′(x) + g′(x)</p>
5
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Difference Rule

d/dx[f(x) − g(x)] = f′(x) − g′(x)

<p>d/dx[f(x) − g(x)] = f′(x) − g′(x)</p>
6
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Product Rule

d/dx[f(x)g(x)] = f′(x)g(x) + f(x)g′(x)

<p>d/dx[f(x)g(x)] = f′(x)g(x) + f(x)g′(x)</p>
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Quotient Rule

d/dx[f(x)/g(x)] = [g(x)f′(x) − f(x)g′(x)]/[g(x)]²

<p>d/dx[f(x)/g(x)] = [g(x)f′(x) − f(x)g′(x)]/[g(x)]²</p>
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Chain Rule

d/dx[f(g(x))] = f′(g(x))·g′(x); differentiate outside, keep inside, multiply by inside derivative.

<p>d/dx[f(g(x))] = f′(g(x))·g′(x); differentiate outside, keep inside, multiply by inside derivative.</p>
9
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General Power Rule

d/dx[u^n] = n·u^(n−1)·u′

<p>d/dx[u^n] = n·u^(n−1)·u′</p>
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Derivative of sin x

cos x

<p>cos x</p>
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Derivative of cos x

−sin x

<p>−sin x</p>
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Derivative of tan x

sec² x

<p>sec² x</p>
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Derivative of cot x

−csc² x

<p>−csc² x</p>
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Derivative of sec x

sec x·tan x

<p>sec x·tan x</p>
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Derivative of csc x

−csc x·cot x

<p>−csc x·cot x</p>
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Derivative of sin u

cos u·u′

<p>cos u·u′</p>
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Derivative of cos u

−sin u·u′

<p>−sin u·u′</p>
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Derivative of tan u

sec² u·u′

<p>sec² u·u′</p>
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Derivative of cot u

−csc² u·u′

<p>−csc² u·u′</p>
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Derivative of sec u

sec u·tan u·u′

<p>sec u·tan u·u′</p>
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Derivative of csc u

−csc u·cot u·u′

<p>−csc u·cot u·u′</p>
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Derivative of e^x

e^x

<p>e^x</p>
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Derivative of e^u

e^u·u′

<p>e^u·u′</p>
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Derivative of ln x

1/x, for x > 0

<p>1/x, for x &gt; 0</p>
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Derivative of ln u

u′/u, for u > 0

<p>u′/u, for u &gt; 0</p>
26
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Trig derivative angle units

Radians

<p>Radians</p>