Calc BC

Definition of a derivative

Product Rule

Quotient Rule

derivative of sin(x)

cos(x)

Derivative of cos(x)

-sin(x)

Derivative of tan(x)

sec²(x)

Derivative of sec(x)

sec(x)*tan(x)

Derivative of csc(x)

-csc(x)*cot(x)

Derivative of cot(x)

-csc²(x)

Chain Rule

F(x) = f(g(x)); f’(g(x)) * g’(x)

Derivative of a^x where a is a constant

a^x * ln(a)

Derivative of inverse sin(x)

Derivative of inverse cos(x)

Derivative of inverse tan(x)

Derivative of inverse csc(x)

Derivative of inverse sec(x)

Derivative of log a of x

Derivative of ln(x)

Rolle’s Theorem

Let f satisfy…

1. f is continuous on closed interval [a,b]

2. f is differentiable in open interval (a,b)

3. f(a) = f(b)

Then there is a number d such that f’(d) = 0

Fermat’s Theorem

If f has a local max or min at d and f’(d) exists, f’(d) = 0

Closed Interval Method

This finds extreme minimums and maxes of continuous functions on interval [a,b]

1. Find values of f at critical values of interval

2. Find values of f at endpoints on interval

3. Largest value of steps 1 and 2 is absolute max and smallest is absolute min

Integral of 1/x

ln(x): d in absolute value

Integral of e^nx

Integral of sin(nx)