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Derivatives
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Calculus
Derivatives & Differentiation
12th
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31 Terms
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1
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f(x)g(x)= . .
f’(x)g(x)+f(x)g’(x) (\**Product Rule*\*)
2
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f(x)/g(x)= . . .
f’(x)g(x)-f(x)g’(x)/(g(x))² (\**Quotient Rule*\*)
3
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d/dx\[f(g(x))\]= . . .
f’(g(x))g’(x) (\**Chain Rule**)
4
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d/dx(cf/(x))= . . .
cf’(x)
5
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d/dx(x^n)= . . .
nx^n-1
6
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d/dx(f(x)__+__g(x))= . . .
f’(x)__+__g’(x)
7
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d/dx(c)= . . .
0
8
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d/dx(e^g(x))= . . .
g’(x)e^g(x)
9
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d/dx\[ln(g(x))\]= . . .
g’(x)/g(x)
10
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d/dx\[sin(x)\]= . . .
cos(x)
11
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d/dx\[cos(x)\]= . . .
\-sin(x)
12
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d/dx\[csc(x)\] = . . .
\-csc(x)cot(x)
13
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d/dx\[sec(x)\]= . . .
sec(x)tan(x)
14
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d/dx\[tan(x)\]= . . .
sec²(x)
15
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d/dx\[cot(x)\]= . . .
\-csc²(x)
16
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d/dx\[sin⁻¹(x)\]= . . .
1/√1-x²
17
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d/dx\[cos⁻¹(x)\]= . . .
\-1/√1-x²
18
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d/dx\[csc⁻¹(x)\]= . . .
\-1/lxl√1-x²
19
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d/dx\[sec⁻¹(x)\]= . . .
1/lxl√1-x²
20
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d/dx\[tan⁻¹(x)\]= . . .
1/1+x²
21
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d/dx\[cot⁻¹(x)\]= . . .
\-1/1+x²
22
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d/dx\[a^x\]= . . .
a^x(ln(a))
23
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d/dx\[ln(x)\]= . . .
1/x, x>0
24
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d/dx\[lnlxl\]= . . .
1/x, x~~*=0*~~
25
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d/dx\[log\[a\](x)\]= . . .
1/x(ln(a)), x>0
26
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d/dx\[sinh(x)\]= . . .
cosh(x)
27
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d/dx\[cosh(x)\]= . . .
sinh(x)
28
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d/dx\[tanh(x)\]= . . .
sech²(x)
29
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d/dx\[csch(x)\]= . . .
\-csch(x)coth(x)
30
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d/dx\[sech(x)\]= . . .
\-sech(x)tanh(x)
31
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d/dx\[coth(x)\]= . . .
\-csch²(x)