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Derivative Rules
A list of derivative rules
19
Mathematics
Undergraduate 2
10/30/2014
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Term
f(x) = ex
 Definition
f'(x) = ex
Term
f(x) = ln(x)
 Definition

f'(x) = 1/x

 

 
Term
f(x) = ax
 Definition
f'(x) = ax ln(a)
Term
f(x) = logax
 Definition
f'(x) = 1/x ln(a)
Term
f(x) = sin(x)
 Definition
f'(x) = cos(x)
Term
f(x) = cos(x)
 Definition
f'(x) = -sin(x)
Term
f(x) = tan(x)
 Definition
f'(x) = sec2(x)
Term
f(x) = cot(x)
 Definition
f'(x) = -csc2(x)
Term
f(x) = sec(x)
 Definition
f'(x) = sec(x)tan(x)
Term
f(x) = csc(x)
 Definition
f'(x) = -csc(x)cot(x)
Term
(f ±g)' = ?
 Definition
f' ± g'
Term
(f•g) = ?
 Definition
f'•g + f•g'
Term
f/g = ?
 Definition
(f'•g - f•g')/g2
Term
f(g(x)) = ?
 Definition
f'(g(x))•g'(x)
Term
f(x) = sin-1(x)
 Definition
f'(x) = 1/(√(1/x2))
Term
f(x) = cos-1(x)
 Definition
f'(x) = -(1/(√(1/x2)))
Term
f(x) = tan-1(x)
 Definition
f'(x) = 1 / (1+x2)
Term
f(x) = sec-1(x)
 Definition
f'(x) = 1 / (|x| √(x2-1))
Term
f(x) = csc-1(x)
 Definition
f'(x) = -(1 / (|x| √(x2-1)))
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