AP Calc Trig, Log, Normal Derivative Rules

F (x) = Sin x

F’ (x) = Cos x

F (x) = Cos x

F’ (x) = -Sin x

F (x) = Tan x

F’ (x) = Sec² x

F (x) = Cot x

F’ (x) = -Csc² x

F (x) = Sec x

F’ (x) = Sec x ⋅ Tan x

F (x) = Csc x

F’ (x) = -Csc x ⋅ Cot x

F (x) = b^x

F’ (x) = b^x ⋅ ln b

F (x) = e^x

F’ (x) = e^x

#^x

#^x * ln#

F (x) = log_b x

F’ (x) = 1/(x ⋅ ln b)

F (x) = ln x

F’ (x) = 1/x

Add/Sub Rule - [f(x)+g(x)] d/dx

f’(x) + g’(x)

Product Rule - [f(x)*g(x)] d/dx

[f’(x) * g(x)] + [g’(x) * f’(x)]

Quotient Rule - [f(x)/g(x)] d/dx
f(x)=hi
d(x)=lo

g(x )* f’(x) - f(x) * g’(x) / g(x)²
lodihi minus hidilo over lolo

Power Rule - [x^n] d/dx

n * x^(n-1)

Coeffiecient Rule - [k*f(x)] d/dx

k * f’(x)

Constant Rule - [k] d/dx

0

arc

inverse of trig identity

d/dx [sin^-1(x)]

d/dx [cos^-1(x)]

d/dx [tan^-1(x)]

d/dx [sec^-1(x)]

d/dx [csc^-1(x)]

d/dx [cot^-1(x)]