Calculus AB

Power Rule

100

Derive: x²

2x

200

Derive: x³

3x²

300

Derive: x¹⁰

10x⁹

400

Derive: 3x¹²

36x¹¹

500

Derive: 9x⁶

54x⁵

Product/Quotient Rule

100

Let g be a function such that g(4)=8, and g'(4)=-3

Let h be the function h(x)=x^1/2

Let H be a function defined as H(x)=g(x)⋅h(x)

What is H′(4)=?

-4

200

Table:

x    g(x)    h(x)     g'(x)        h'(x)

0     -3       -1        5             3

F(x)=g(x)⋅h(x)

What is F'(0)=?

-14

300

Derive: cos(x)/sin(x)

-1/sin(x)²

400

Table:

x       g(x)        h(x)        g'(x)       h'(x)

-2       4             1            -1           2

H(x)=g(x)/h(x)

What is H'(-2)=?

H'(-2)=-9

500

Derive: y=x² ln(x)

x+2xln(x)

Trigonometric Functions

100

Derive: sin(x)

cos(x)

200

Derive: cos(x)

-sin(x)

300

Derive: sec(x)

(sec(x))(tan(x))

400

Derive: arcsin(x)

1/(1-x²)^1/2

500

Derive: cot(x)

-csc²(x) or -1/sin(x)²

Chain Rule

100

Derive: sin(x²)

2xcos(x²)

200

Derive: (x²)^1/2

2x/(x²)^1/2

300

Table:

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

1         4            2             3              -2

2          6            1            1                0

G(x)=f(g(x)), what is G'(2)?

G'(2)=0

400

f(x)= -5 x 7^x

Find f '(x)

-5 x 7^x ln(7)

500

y= tan(x² - 4x)

Find dy/dx (Derivative) 

2x - 4 / cos²(x² - 4x)