Calculus—Derivatives to Memorize
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f(x)=e^u
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f’(x)=e^u×du
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f(x)=a^u
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f’(x)=a^u×ln(a)×du
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16 Terms
1
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f(x)=e^u
f’(x)=e^u×du
2
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f(x)=a^u
f’(x)=a^u×ln(a)×du
3
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f(x)=sin(u)
f’(x)=cos(u)×du
4
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f(x)=tan(u)
f’(x)=sec²(u)×du
5
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f(x)=sec(u)
f’(x)=sec(u)×tan(u)×du
6
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f(x)=ln(u)
f’(x)=1/u×du OR du/u
7
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f(x)=loga(u)
f’(x)=1/u×ln(a)×du OR du/u×ln(a)
8
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f(x)=cos(u)
f’(x)=-sin(u)×du
9
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f(x)=cot(u)
f’(x)=-csc²(u)×du
10
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f(x)=csc(u)
f’(x)=-csc(u)×cot(u)×du
11
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arcsin(x)/sin⁻¹(x)
1/√1-x²
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arccos(x)/cos⁻¹(x)
-1/√1-x²
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arcsec(x)/sec⁻¹(x)
1/|x|√x²-1
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arccsc(x)/csc⁻¹(x)
-1/|x|√x²-1
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arctan(x)/tan⁻¹(x)
1/1+x²
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arccot(x)/cot⁻¹(x)
-1/1+x²