Calc 1 Jeopardy

Trig Function Derivatives

100

Derivative of sin(x)

cos(x)

200

Derivative of cos(x)

-sin(x)

300

Derivative of tan(x)

sec^2(x)

400

Derivative of sec(x)

sec(x)tan(x)

500

Derivative of cot(x)

-csc^2(x)

ArcTrig Derivatives

100

Derivative for arcsin(x)

1/(1-x^2)^1/2

200

Derivative for arccot(x)

-1/(1+x^2)

300

Derivative for arctan(x)

1/(1+x^2)

400

Derivative for cosh(x)

sinh(x)

500

Derivative for arccsc(x)

-1/(x(x^2-1)^1/2)

Exam 1 Review

100

What does a derivative represent?

Slope of the tangent line/specific point

200

Define Continuity rule (what are the steps?)

The limit and function both exist, and they are equal to each other.

300

Name 3 types of discontinuities

Hole, jump, asymptote

400

What does IVT prove?

A solution exists

500

What is the equation for solving derivatives by limit definition

(f(x-h)-f(x))/h as h approaches 0

Power Rule

100

x^5

4x^4

200

4x^3

12x^2

300

x^-2

-2/x^3

400

1/sqrt(x)

1/2x^3/2

500

5x^3/2-1/x

15sqrt(x)/2+1/x^2