AP Calc AB Unit 2B Formulas

d/dx of an Inverse Function

g’(x) = 1/f’(g(x))

d/dx arcsinu

du/(1-u²)

d/dx arccosu

-du/(1-u²)^1/2

d/dx arctanu

du/1+u²

d/dx arccotu

-du/1+u²

d/dx arcsecu

du/|u|(u²-1)^1/2

d/dx arccscu

-du/|u|(u²-1)^1/2

Derivative of an exponential function

d/dx = a^u lna du/dx

Derivative of the natural logarithm

d/dx (lnu) = 1/u du/dx = u’/u

Derivative of log>2 x

d/dx (log>a u) = 1/ulna du/dx