AP Calc Formula Practice (Mrs. K)

Trig Derivatives

100

Derivative of Cos(x)

-Sin(x)

200

Derivative of Tan(x)

Sec²(x)

300

Derivative of Sec(x)

Sec(x)Tan(x)

400

Derivative of Cot(x)

-Csc²(x)

500

Derivative of Csc(x)

-Csc(x)Cot(x)

Derivative Rules

100

Derivative of any constant number (no x term)

0

200

Product Rule using f(x)g(x)

f'(x)g(x) + g'(x)f(x) (yes, the two can be interchangeable)

300

Quotient rule to f(x)/g(x)

((f'(x)g(x)) - (g'(x)f(x)))/(g(x))²

400

chain rule of f(g(x))

f'(g(x))g'(x)

500

derivative with x in the numerator (use a^x)

ln(a)a^x

Derivatives of Inverse Trig Functions

100

-1/√(1-x²)

the derivative of cos^-1(x)

200

-1/(1+x²)

the derivative of cot^-1(x)

300

1/(1+x²)

the derivative of tan^-1(x)

400

-1/(|x|√(x²-1))

the derivative of csc^-1(x)

500

1/(|x|√(x²-1))

the derivative of sec^-1(x)

Integral Practice Problem

100

indefinite integral of x² + 5

x³/3 + 5x + C

200

Indefinite integral of e^x

e^x + C

300

indefinite integral of 1/x

ln(x)+C

400

indefinite integral of -sin(2x)

(cos(2x))/2 + C

500

Indefinite integral of 4^3x

4^3x/3ln(4) + C

Graphing rules

100

when given the graph of f(x), the derivative is the ___ at the given point

slope

200

A graph is increasing when the derivative is ___ and decreasing when the derivative is ____

positive; negative

300

A function is concave ____ when f''(x) is positive and concave ____ when f''(x) is negative.

up; down

400

point on f(x) when f'(x) = 0

critical point (a max or a min)

500

point where f(x) changes from concave up to concave down

point of inflection