Calculus

Derivatives

100

What is the derivative of x²?

2x

200

What rule is used to differentiate f(x)g(x)?

Product Rule

300

Find d dx(sin⁡x).

cos⁡x

400

Find the derivative of 3e^x?

3ex

500

Find ddx(x³ln⁡x).

3x2ln⁡x+x2

Chain Rule

100

Find ddx((x²+1)3).

3(x²+1)2(2x)

200

Find ddx(sin⁡(x²).

cos⁡(x²)(2x)

300

Find ddx(e^3x).

3e^3x

400

Find ddx(ln⁡(5x+2)).

55x+2

500

Find ddx(4x³+2).

124x³+2(12x²)

Limits

100

What does lim⁡x→∞1x equal?

0

200

What is the limit of a constant?

The constant

300

lim⁡x→0sin⁡x(x)

1

400

What method is used to evaluate 00 limits?

L'Hôpital’s Rule

500

lim⁡x→2x2−4x−2

4

Applications

100

What does a derivative represent?

Rate of change

200

What does an integral represent?

Area under a curve

300

What is the slope of a tangent line?

The derivative at a point

400

What is the second derivative used for?

acceleration

500

What is a critical point?

Where f′(x)=0 or undefined

Theorems

100

What theorem connects derivatives and integrals?

Fundamental Theorem of Calculus

200

What theorem guarantees a root between two points?

Intermediate Value Theorem

300

What theorem guarantees a horizontal tangent?

Mean Value Theorem

400

What theorem says continuous functions on closed intervals have max/min?

Extreme Value Theorem

500

What theorem is used for linear approximations?

Taylor’s Theorem