AP Calc AB Unit 3

dy/dx horizontal/vertical tangent lines

Horizontal at dy/dx = 0
Vertical at dy/dx = undefined

derivative of an inverse function

1/f’ (f^-1(b))

d/dx arcsin(x)

1 / √(1 - x²)

d/dx arccos(x)

-1/√(1-x²)

d/dx arcsec(x)

1 / (|x| × √(x² - 1))

d/dx arccsc(x)

-1 / (|x| × √(x² - 1))

d/dx arctan(x)

1 / (x² + 1)

d/dx arccot(x)

-1 / (x² + 1)

d/dx e^u

e^u x du/dx

d/dx a^u

a^u ln(a) x du/dx

d/dx ln(u)

1/u x du/dx

d/dx loga u

1/u(ln(a)) x du/dx

d/dx ln |x|

1/u x du/dx