Calc Review: Mrs. Miz

Solve the Derivatives

100

y = 3x^2

y' = 6x

200

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

y' = 6x^2 - 6x + 1

300

y = e^(2x)

y' = 2e^(2x)

400

y = sin(x) * cos(x)

y' = cos^2(x) - sin^2(x)

500

y = ln(x^2 + 1)

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

Solve the Integrals

100

∫ 2x dx

x^2 + C

200

∫ (x^3 + 2x - 1) dx

(1/4)x^4 + x^2 - x + C

300

∫ (2x * e^x) dx

2x*e^x - 2e^x + C

400

∫ e^(3x) * sin(2x) dx

1/5 * e^(3x) * (3sin(2x) - 2cos(2x)) + C

500

∫ x^4 / (1 + x^2) dx

1/2 * x^3 - x + arctan(x) + C

Evaluate the Limit

100

lim (x -> 3) 2x - 1

5

200

lim (x -> 0) (x^2 - 1) / (x - 1)

-1

300

lim (x -> 1) (sqrt(x) - 1) / (x - 1)

1/2

400

lim (x -> 0) sin(x) / x

1

500

lim (x -> 0) (e^x - 1 - x) / x^2

1/2

Find the equation of the Tangent line

100

y = x^2 at x = 1

y = 2x - 1

200

y = 2x^2 + 3 at x = 2

y = 8x - 5

300

y = -x^2 + 4x + 3 at x = 3

y = -2x + 12

400

y = 3x^2 - 2x + 1 at x = 1

y = 4x - 2

500

y = x^2 - 4x + 7 at x = 2

y = 3

Rules

100

This rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g

Chain Rule

200

This rule is a formula used to find the derivatives of products of two or more functions.

Product Rule

300

This rule is used to differentiate functions of the form f(x) = x^r, whenever r is a real number.

Power rule

400

This rule says that the limit when we divide one function by another is the same after we take the derivative of each function

L’hopitals Rule

500

Thi rule is a method of finding the derivative of a function that is the ratio of two differentiable functions.

Quotient rule