Derivative and Integral Rules

AP Calculus AB

Derivative of sin(u)

cos(u) * du/dx

Derivative of tan(u)

sec²u * du/dx

Derivative of sec(u)

sec(u)*tan(u)*du/dx

Derivative of ln(u)

u’/u

Derivative of e^u

e^u*du/dx

Derivative of arcsin(u)

u’/sqrt(1-u²)

Derivative of arctan(u)

u’/|u|sqrt(u²-1)

Derivative of cos(u)

-sin(u)

Add a “co” to the derivatives of tangent and secant when asked for the derivative of cotangent and cosecant.

ok cos!

Derivative of log_au

1/ln(a) * u’/u

Derivative of a^u

x^u*u’*lnx

Adding a cotangent to the inside of the arc derivatives just turns the derivative answer into a negative.

ok negatives!