APEX Calculus

Derivative Rules

100

The Power Rule for Derivatives.

nx^{n-1}

200

The Constant Multiple Rule for Derivatives

(cf(x))' = cf'(x)

300

What is the product rule?

f'g+g'f

400

What is the quotient rule?

f'g-g'f/ g²

500

Write the chain rule

(f’ º g) × g’

Trig

100

Derivative of sinx

cosx

200

Derivative of tanx

sec²x

300

Derivative of cscx

-cscxcotx

400

Antiderivative of sinx

-cosx+C

500

Antiderivative of csc^2(x).

-cot(x)+C

Components of the Derivative

100

What does the graph of the derivative describe?

It shows all the slopes of lines tangent to the original graph

200

What does it mean when f'(x)= 0

A maximum, minimum, or critical point

300

How do you decided whether a critical point is a maximum or minimum?

Positive to negative = max; negative to positive =min

400

What does it mean when f''(x)= 0

potential inflection point

500

How do you figure out when the original graph, f(x), is concave up?

When f''(x)>0

Antiderivatives

100

Find the antiderivative of x^2

x^3/3+c

200

What is reverse power rule?

1/(n+1)x^(n+1)

300

Find the antiderivative of sec^2(x)

tan(x)+c

400

Find the antiderivative of 1/x+3x^(1/2)

ln(x)+2x^(3/2)+c

500

f''(x)=3x, f'(2)=1, f(4)=5

Find f(x)

f(x)=1/2x^3-5x-7