Calculus AB Jeopardy

Derivatives 1

100

y = x

dy/dx = 1

200

y = -x^2 + 3

dy/dx = -2x

300

y = 5x^3 - 3x^5

dy/dx = 15x^2 - 15x^4

400

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

dy/dx = 4x^2 - 1

500

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

dy/dx = x^2 + x + 1/4

Derivatives 2

100

y = 4 - 2x - x^-3

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

200

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

dy/dx = -6x^-3 + (1/z^2)

300

y = -2x^-1 + 4/x^2

dy/dx = (2 / x^2) - (8 / x^3)

400

y = 6x^2 - 10x - 5x^-2

dy/dx = 12x - 10 + 10 / x^3

500

y = (1/3x^2) - (5/2x)

dy/dx = -2/3x^3 + 5/2x^2

Derivatives 3

100

y = (3 - x^2)(x^3 - x - 1)

dy/dx = -5x^4 + 12x^2 - 2x - 3

200

y = (x^2 + 1)(x + 5 + 1/x)

dy/dx = 3x^2 + 10x + 2 - 1/x^2

300

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

3x^2

400

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

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

500

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

dy/dx = 2x + 1 - 1/x^2 + 2/x^3

Derivatives 4

100

y = -10x + 3cosx

dy/dx = -10 - 3sinx

200

y = (3/x) + 5sinx

dy/dx = (-3/x^2) + 5cosx

300

y = (cosx) / (1 + sinx)

dy/dx = -1/1 + sinx

400

y = x^2cosx - 2xsinx - 2cosx

dy/dx = x^2sinx

500

y = tanx - x

dy/dx = sec^2(x) - 1 or tan^2(x)

Derivatives 5

100

y = (e^x) / (e^x - 1)

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

200

y = e^x / x

dy/dx = ((e^x) / (x)) - ((e^x) / (x^2))

300

y = 2x^((1/2)-e)

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

400

y = (e^3x)(cos(2x))

dy/dx = (e^3x)(3cos2x - 2sin2x)

500

y = (x^2)(2^x) + 1^2

dy/dx = (2^x)(2x + (x^2)(ln2))