Calculus BC Unit 3

Chain Rule

100

f(x) = 5sin(6x + 11). What is f'(x)?

30cos(6x + 11)

100

f(x) = 5(18x - 17)³; what is the derivative?

270(18x - 17)²

100

f(x) = 3ln(6x - 1/2); f'(x) = ?

3_{/6x - 1/2}

100

16cos(5x + 17)

-80sin(5x + 17)

Inverse Functions

100

true or false: sin^-1(x) is the same as arcsin(x)

true

100

derivative of tan^-1(x)?

1/(x² + 1)

100

derivative of sin^-1(x)?

1/_{square root(x}² _{- 1)}

100

What is the derivative of cot^-1(5x² + 12)?

-10x/(25x⁴ + 145)

Higher Order Derivatives

100

f(x) = 5x³ + 24x - 16; find f''(x)

30x

100

f(x) = 2x⁵ - 14x³ + 16x² - 14; find f''(x)

40x³ - 84x + 32

100

f(x) = 4x⁴ - 16x³ - 17x² + 2; find f'''(x)

96x - 96

100

f(x) = 3x⁵ + 6x⁴ - 3x³ - 12x² + 10; what is f'''(x)?

180x² + 144x - 19

Implicit Differentiation

100

Find dy/dx: x² + y² = 36

-x/y

100

Find dy/dx: xy - y = 527

-y/(x - 1)

100

find dy/dx: x³ + y³ = xy

(y - 3x²) / (3y² - x)

100

find dy/dx: cos(x)² + sin(y)³ = 6

(2xsin(x²)) / (3y²cos(y³))