Derivative Jeopardy

Power Rule

100

x² + 2x + 3

2x + 2

200

x⁴ + 7pi

4x³

300

x^3/2 +4x²

3/2x^3/2 + 8x

400

2x^-4 - e^3x

-8/x⁵ - 3e^3x

500

7lnx + 5sqr.(x)  

7/x + 5/2sqr.x 

Chain Rule

100

(ln x)⁷

7(ln x)⁶  / x

200

Sqrt.(x³+7)

3x/2sqrt.(x³+7)

300

e^2ln(3x)

6e^2ln(3x)/3x

400

ln(cos(e^3x))

-3e^3xsin(e^3x) / cos(e^3x)

500

Sin⁵(tan(cos(x³)))

-3x²sin(x³)sec²(cos(x³))4cos(tan(cos(x³)))

Product Rule

100

(2x-4)(x+3)

(2x+6) + (2x-4) 

200

(x³)lnx + 4

3x² lnx + x²

300

sqrt.(x)(x²+7x-2) 

(x²+7x-2)/ 2sqrt.(x) + sqrt.(x)(2x+7) 

400

5cosxtanx

5cosxsec²x - 5sinxtanx

500

sinx(8e^x +3) 

cosx(8e^x+3) + sinx(8e^x)

Quotient Rule

100

(e^x + 5)/x²

(x²(e^x) - 2x(e^x + 5))/x⁴

200

(4x² + 7x + 13)/(5x + 6)

((5x + 6)(8x - 7) - (4x² + 7x + 13)(5))/(5x+6)²

300

(2sqrt(x) + 3x)/(10x³ - 9x² + 8)

((10x³ - 9x² + 8)(x^-1/2 + 3) - (2sqrt(x) + 3x)(30x² - 18x))/(10x³ - 9x² + 8)²

400

(e^{x^2 + 2x} - 9x + 6x²)/(7x³ + 2x)

(((e^{x^2 + 2x})(2x+2) - 9 +12x)(7x³ + 2x)) - ((e^{x^2 + 2x} - 9x + 6x²)(21x² + 2))/(7x³ + 2x)²

500

(sin(5x²) + 10)/(tan(3x⁴ + x³)

(tan(3x⁴ + x³))(10xcos(5x²)) - (sin(5x²) + 10)((12x³ + 3x²)sec²(3x⁴ + x³))/(tan(3x⁴ + x³))²