Derivative Jeopardy!

Basic Derivative

100

What is the definition of a derivative. 

The instantaneous rate of change

200

What is the notation for a derivative?

f'(x)

or 

dy/dx

300

20x^2

40x

400

5x^3 + 10x^2 + 50x

15x^2 + 20x + 50

500

57x^7-23x^5-15x^3+8x+2

399x^6-115x^4-45x^2+8

Chain Rule

100

f(x)=(2x^2 +5)^5

20(2x^2 +5)^4

200

f(x) = (4t^2−3t+2)^2−2

f'(x)=2(8t−3)(4t^2−3t+2)

300

f(x)=4(1+7x)^9

f'(x)=252(1+7x)^8

400

b(y)=(y^3-5)^-4

B'(y)=-12y^2/(y^3-5)^5

500

f(x)=(2x-3)^4 (x^2+x+1)^5

f'(x)=8(2x-3)^3 (x^2+x+1)+(2x^3-x^2-x-3)64(10x+5)

Product Rule

100

f(x)=(x^2-1)(x+5)

f'(x)=3x^2+10x-1

200

y=2(6-x^2)^5

y'=10(6-x^2)^4(-2x)

300

f(x)=(3x2 – 1)(x2 + 5x +2)

f'(x)=12x^3+45x^2+10x-5

400

f(x)=(x^2-2)(x^-1+2)

f'(x)=4x+2x^-2+1

500

f(x)=(2x^4-2x^2+2)(5x^4+1)

f'(x)=8x^7-60x^5+48x^3-4x

Quotient Rule

100

y=x^2/(x^2-3)

dy/dx=(-6x)/(x^2-3)^2

200

y=(2-x)/(3x+1)

dy/dx=-7/(3x+1)^2

300

y=2/(5x+1)

y'=-30/(5x+1)-4

400

y=(2x^3)/(4-x)

dy/dx=(24x^2-4x^3)/(4-x)^2

500

y=(x^2 +x-2)/(x^3 + 6)

dy/dx=(-x^4 - 2x^3 + 6x^2 + 12x+6)/(x^3 +6)^2

More examples (mixed)

100

f'(x)=4x^5

f'(x)=20x^4

200

h(t)=2/(2t^2-3)

h'(t)=(-8t)/(2t^2-3)^2

300

f(x)=(1+x^-4)(x^5 +5)

f'(x)=(5x^4+1- 20)/x^5

400

y=sqrt(5x^3)/(5x^3)

dy/dx=(5/2x(5x^(-1/2))-(5x)^(1/2))/x^2

500

h(u)=sqrt(u-1) sqrt(2u+3))

h'(u)=1/2(u-1)^(-1/2)(2u+3)^(1/2)+(2u+3)^(-1/2)(u-1)^(1/2)