Calculus Jeopardy Game

Product Rule

100

What is the product rule?

f(x) = u(x)*v(x)

f’(x) = u(x)*v’(x) + v(x)*u’(x) 

200

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

f’(x) = 3x^2 + 10x -1

300

f(x) = (x + 5)(3x - 2)

f’(x) = 6x + 13

400

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

f’(x) = 4x^2 e^x + 8xe^x - 2

500

f(x) = x^2 lnx

f’(x) = x(2lnx + 1)

L’ Hospital’s Rule

100

Lim x—> 0

(sin5x) / (x)

5

200

Lim x —> 3

(x - 4）/ （x - 2)

-1

300

Lim x —>

(x^3 - 8) / (x^2 - 4)

3

400

Lim x —> pi/2

(1-sinx) / (1 + cos2x)

1

500

Lim x —> 1

(x^3 - 1) / (4x^3 - x - 3)

3/11

Implicit Differentiation

100

3x^2 + 5y^2 = -y + 2

dy/dx = -6x / 10y+1

200

y = 4x^2 + 5y^3

dy/dx = 8x / 1 - 15y^2

300

4y^3 = 2x^3 + 3xy^3

dy/dx = 2x^2 + y^3 / 4y^3 - 3y^2x

400

2x + 3x^3 y^2 = 5x^2 y at (1,1)

dy/dx = -1

500

-4x^2 y + 4 = 5x^2 + 3x^3 y^2 at (1, -1)

dy/dx = 11/2

Quotient Rule

100

What is the quotient rule?

f(x) = u(x) / v(x)

f‘(x) = v(x)u’(x) - u(x)v’(x) / v(x)^2

200

y = (4-5x) / (x^2 + 3)

f’(x) = -15 - 4x / (x^2 + 3)^2

300

f(x) = x^2 + 1 / e^x

f’(x) = 2xe^x - x^2 e^x - e^x / (e^x)^2

400

f(x) = sinx / 2x^2 - 5

f’(x) = cosx(2x^2 - 5) - sinx(4x) / (2x^2 - 5)^2

500

f(x) = 3x / x+x^2

f’(x) = (x + x^2)(3) - (3x)(1 + 2x) / (x + x^2)^2

Power Rule

100

What is the power rule?

f(x) = ax^n

f’(x) = (a * n) x^n-1

200

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

f’(x) = 3x - 2

300

f(x) = –2x^2 + 3x - 5

f’(x) = -4x + 3

400

f(x) = 15x^5 - 8x^2 - 4x

f‘(x) = 75x^4 - 16x - 4

500

f(x) = 100x^7 - 26x^6 + 16x^4

f’(x) = 700x^6 - 156x^5 + 64x^3