DERIVATIVE JEOPARDY

POWER RULE

100

2x²

4x

200

8x³ + 1/2x - 4/3 

24x² + 1/2

300

7x⁵ − 4x³ + 1/3x² + 6

35x⁴ - 12x² + 2/3x

400

1/x⁴ + 4x³ - 12/3x² - 5/8

-4x^-5 + 12x² - 8x

500

5x⁷ − 3x^4.5 + 2x^-3 + (1/√x) − 9

35x⁶ - 13.5x^3.5 - 6x^-4 - 0.5x^-1.5

PRODUCT RULE

100

(3x²)(5x³)

75x⁴

200

(2x³ − 5x)(x² + 4)

10x⁴+9x²−20

300

(x³ + 2x²)(5x⁴ − x + 7)

(3x² + 4x)(5x⁴ − x + 7) + (x³ + 2x²)(20x³ − 1)

400

(x⁴ + 3x²)(sin(x) + x³)

7x⁶ + 16x⁴ + 4x³ sin(x) + 6x sin(x) + x⁴ cos(x) + 3x² cos(x)

500

(x² + 5x)(e^xcos(x))

e^xcos(x)(2x + 5) + e^x[cos(x) − sin(x)](x²+5x)

QUOTIENT RULE

100

x^2
____
x

1

200

x^2
________
x + 1

x²+2x
^_________
(x + 1)²

300

3x² + 2x
^____________
x³ − 1

−3x⁴ − 4x³ − 6x − 2
^{________________________}
(x³ − 1)² 

400

√(x) + 1
^_________
sin(x)

sin(x)⋅1/(2√x) − (√(x) + 1)⋅cos(x)
^{____________________________________}
sin²(x)

500

 x⁴ln(x)
^__________
2x³ + 1

  2x⁶ln(x) + 2x⁶ + 4x³ln(x) + x^{3
____________________________________}
(2x³ + 1)²

CHAIN RULE

100

(3x + 2)⁴

12(3x + 2)³

200

sin(3x² + 5x)

cos(3x² + 5x)(6x + 5)

300

[cos(x²)]³

−6x⋅cos²(x²)⋅sin(x²)

400

[sin(x² + 1)³]⁴

24x⋅(sin(x² + 1)³)³⋅sin(x² + 1)²⋅cos(x² + 1)

500

[tan(5x³ + 2x)]⁶

6(15x² + 2)⋅tan⁵(5x³ + 2x)⋅sec²(5x³ + 2x)

RANDOM

100

-sin(7x)

-14cos(7x²)

200

(x²)(cos(4x))

1/(2√x)cos(4x) − 4x²sin(4x)

300

√(x)⋅cos(x³)

1/(2√x)cos(x³) − 3x^5/2sin(x³)

400

(x² + 1)³⋅sin(x)
^{____________________}
x

6x²(x² + 1)2sin(x) + x(x² + 1)3cos(x) − (x² + 1)3sin(x)
^{___________________________________________________________________}
x²

500

√(x² + 4)⋅sin(x³)
^{____________________}
x² + 1

(x² + 1)⋅[x/√(x² + 4)sin(x³) + √(x² + 4)⋅3x²cos(x³)] − 2x√(x² + 4)⋅sin(x³)
________________________________________________________________
(x² + 1)²