Basic rules
Constantd/dx (c) = 0c = constant
Power ruled/dx (xⁿ) = n·xⁿ⁻¹x > 0 for general real n; any x if n is a positive integer
Constant multiple(c·f)′ = c·f′c = constant
Sum / difference(f ± g)′ = f′ ± g′
Product rule(fg)′ = f′g + fg′
Quotient rule(f/g)′ = (f′g − fg′) / g²where g ≠ 0
Chain rule(f(g(x)))′ = f′(g(x)) · g′(x)
Trigonometric
x is in radians for all trig rules on this page.
sin xd/dx (sin x) = cos x
cos xd/dx (cos x) = −sin x
tan xd/dx (tan x) = sec²x
sec xd/dx (sec x) = sec x · tan x
cosec xd/dx (cosec x) = −cosec x · cot x
cot xd/dx (cot x) = −cosec²x
Exponential & logarithmic
e^xd/dx (eˣ) = eˣ
a^xd/dx (aˣ) = aˣ · ln aa > 0, a ≠ 1
ln xd/dx (ln x) = 1/xx > 0
log base ad/dx (logₐ x) = 1 / (x · ln a)x > 0, a > 0, a ≠ 1
Square rootd/dx (√x) = 1 / (2√x)x > 0
