Basic Derivative Rules

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17 Terms

1
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Derivative of Constant

d/dx[c] = 0

<p>d/dx[c] = 0</p>
2
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Sum/Difference

d/dx[f (x) ± g(x)] = f ′(x) ± g′(x)

<p>d/dx[f (x) ± g(x)] = f ′(x) ± g′(x)</p>
3
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Product Rule

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

<p>d/dx[f (x) · g(x)] = f (x)g′(x) + g(x)f ′(x)</p>
4
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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>
5
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Chain Rule

d/dx[f (g(x))] = f ′(g(x))g′(x)

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

d/dx[u^n] = n u^(n−1) u′

<p><span>d/dx[u^n] = n <em> u^(n−1) </em> u′</span></p>
7
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Exponential Rules

d/dx[e^u] = e^u * u' / d/dx[a^u] = ln(a)a^u * u'

<p>d/dx[e^u] = e^u * u' / d/dx[a^u] = ln(a)a^u * u'</p>
8
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Logarithmic Rules

d/dx[ln(u)] = u'/u / d/dx[log b (u)] = u' / u ln b

<p>d/dx[ln(u)] = u'/u / d/dx[log b (u)] = u' / u ln b</p>
9
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derivative of sin(u)

cos(u) * u’

<p>cos(u) * u’</p>
10
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derivative of cos(u)

-sin(u) * u’

<p>-sin(u) * u’</p>
11
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derivative of tan(u)

sec²(u) * u’

<p>sec²(u) * u’</p>
12
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derivative of csc(u)

− csc(u) cot(u) * u′

<p><span style="font-size: calc(var(--scale-factor)*9.96px)">− csc(u) cot(u) * u</span><span style="font-size: calc(var(--scale-factor)*6.97px)">′</span></p>
13
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derivative of sec(u)

sec(u) tan(u) * u′

<p>sec(u) tan(u) * u′ </p>
14
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derivative of cot(u)

−csc²(u) * u'

<p>−csc²(u) * u' </p>
15
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derivative of (sin^-1 x)

u’ / √(1 - u²)

<p>u’ / √(1 - u²) </p>
16
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derivative of (cos^-1 x)

-u’ / √(1 - u²)

<p>-u’ / √(1 - u²) </p>
17
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derivative of (tan^-1 x)

u’ / 1 + u²

<p>u’ / 1 + u²</p>

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