AP Calculus AB WCTA - Evelyn Murillo

Derivative

100

15x⁷

105x⁶

200

2x²*4x⁴

48x⁵

300

3x⁷/2x⁸

-3/2x²

400

(x³+2x)⁴

4(x³+2x)³(3x²+2)

500

(8x³*2x⁵)⁴

2097152x³¹

Antiderivative

100

∫2x⁵dx

1/3x⁶

200

∫1-3x²-6x dx

x - x³ - 3x² + c

300

∫3x²*4x⁴dx

12x⁷/7 + C

400

∫sin(2x)4x²dx

-2x²cos(2x)+2xsin(2x)+cos(2x)+c

500

∫(2x^{2e^3})dx

(2/2e³+1)x^{(2e^3)+1+c}

Product Rule

100

−x³(3x⁴ − 2)

-21x⁶+6x²

200

((-2x⁴-3)(-2x²+1))

24x⁵-8x³+12x

300

((2-3x)(x²+5x-1))

-9x²-26x+13

400

(cos(2x²)3x)

3(-4x²sin(2x²)+cos(2x²))

500

(cos(2x²)cos(3x⁴))

-4xsin(2x²)cos(3x⁴)-12x³sin(3x⁴)cos(2x²)

Implicit Differentiation

100

x+y=3x

dy/dx = 2

200

2y+4x² = 3y²-7

dy/dx = -8x/2-6y

300

3xy+4y² = 3x³

dy/dx = 9x²-3y/3x+8y

400

y/x +2y = 3x²

dy/dx = 6x³=y/x+2y

500

2(x+y³)²+2x = 5x²y

dy/dx = 10xy-4x-4y³-2/12xy²+12y³-5x²

Chain Rule

100

(5x⁴+1)²​​​​

40x³(5x⁴+1)

200

(3x-1)(-3x²-4)^-3

3(15x²-6x-4)/(-3x²-4)²

300

(5x⁵-3/-3x³+1)³

3x²(5x⁵-3)²(-30x⁵+25x²-27)/(-3x³+1)⁴

400

(x⁵+4/x²-5)^1/5

x(3x⁵-25x³-8)/5(x⁵+4)^4/5(x²-5)^6/5

500

5√x²-3 /-x-5

3x²-15-10x/5(-x-5)²(x²-3)^4/3