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Average Rate of Change

Chain Rule| dy/dx = f’[g(x)] * g’(x) | dy/dx = f’(u) * u’ | (5x²+7)^5 | sin(ax) | 7*cos(5*x^2) | (tan (5x))^5 Video Example 2

cos(a * x) derivative

cos(a * x) integral

Critical Numbers

Definite Integral| = ∫ [ f (x) ] dx

Definition of a Derivative

Derivative In(x)

Given Delta – Find Epsilon

Derivatives/Algebra (step by step)| √(x) | 3√(x) | 5/√(x) | 5/x | 5/8x | 5/x² | (5x)² | 5x²/8 | x(x+5) | x^½ | x^(-½) | (x²-4)/(x+2) | (x²-4)/(x-2) | (5x²+7)^5 | √(5x²+7) | (5x²+7)½ | ³√ (5x²+7) | (5x²+7)¹/³ | sin | cos | tan

ê(x) Derivatives

ê(x) Integrals

Equation of a Tangent Line (y=mx+b)

Equation of a Line

Equation of a tangent line at a Curve| (y = mx + b)

Fence Area

Graphing by Hand |Concavity | Critical Points | Crosses x axis | Inflection Point | Intervals of Increase | Intervals of Decrease | Local Maximum & Minimum

Implicit differentiation| y³+y²-5y-x² = -4

Inflection Point

Integrals/ Algebra (Rewrite selected & Integrate)| n / √(x) | (x² + n)² | (x³ + n)/x² | ³√(x) | n / x² | n / ³√(x) | n / x√(x) | 1/x³

Integrals – Answer Only

Integration by Parts| ln(x) | n*e^x Video Example | sin(x) | cos(x) | sin(x) and cos(x)

Intervals of Increase or Decrease

Limits |Instructions | Definition | Execute Limit

ln(x)| Derivatives

ln(x)| Integrals

Local Max & Min| Extrema

log(x) Log to Other Base| Evaluate | Solve for x | Exponential Form | Logarithmic Equation | Differentiate | Integrate

Log to Base a

Money

Natural Log| ln(x)

Product Rule |( f (x) )( g (x) )

Quadratic Formula

Quotient Rule| ( f (x ) ) / ( g (x) )

Relative Extrema

sin(a*x) Derivative

sin(a*x) Integral

sin(a*x) Integral

sin(x)^3*cos(x)^2

tan(a*x) Derivative

Trig & Half Angle Formulas & Identities| sin(u)*cos(v) |[1+cos(2x)]/2 | cos(2x)2 | [1-cos(cs)]/2 | 1-cos(2x) / 1+cos(2x) | sin²(x) + cos²(x) = 1 | tan(x) | tan²(x) | Trig d/dx cos(2x)/2 | cos(2x) | cos(x) | cos²(x) | cot(x) | csc(x) | csc²(x) | sec(x) | sec²(x) | sin(2x) | sin(x) | sin²(x)

Trig d/dx Identities

U – Substitution

A & B Vectors A(x,y,z) B(x,y,z) ||A|| Magnitude ||B|| Magnitude | A – B | A – B Magnitude | A + B | A + B Magnitude | A + B + C | Find Resultant | Find Components | A * B Dot Product | | A x B Cross Product | B – A | n * A | (n * A) + (n * B) | Area of a parallelogram | Component A direct B | cosine(AB) | Equation of a Plane | ax+by+cz+d=0 | P&Q Points | Projection of A on B | Projection of B on A | Unit vector A | Unit vector B Video Example 2

Acceleration| r(t) function

Angle of a Vector| r(t) function

Arc Length| f(x) system | r(t) system | y system

Average Rate of Change

Component of A Direction of B

Conservative Curl

Compute Curl at a PointVideo Example

Compute Divergence at a Point

Cosine(∅) of A & B

Curl| Definition | PQR notation | Conservative | Divergence | Curl Problem | Compute Curl at Point | Compute Divergence at Point | MNP notation | Conservative | Divergence | Curl Problem | Compute Curl at Point | Compute Divergence at Point

Divergence of Curl

Divergence of Vector Field

Eliminate the Parameter (t)

Gradient| Definition | 2 Variables | 3 Variables## Green’s Theorem

Trig & Half Angle Formulas| 1 + cos(2x)2 | 1 – cos(2x)/1 + cos(2x) | 1 – cos(2x)/2 | cos(2x) | cos(x) | cos²(x) | cot(x) | csc(x) | csc²(x) | sec(x) | sec²(x) | sin(2x) | sin(x) | sin²(x) | sin²(x) + cos²(x) = 1 | tan(x) | tan²(x)

Linear Approximation (3 variable)| ax+by+cz+d=0

Line Integral Over Range| = ∫ ( f [(x(t),y(t),z(t)] * √ [ x'(t)² + y'(t)² + z'(t)² ] ) dt

Mass of Spring or Wire

Magnitude of a Vector| r(t) function

Parametric Equation |r(t) function

Partial Fraction Decomposition

Polar to Rectangular Conversions

Projection of Vector A on Vector B

P & Q Vector Points| Position Vectors | Projection of a on b, b on a | Speed

Quadratic Formula

Sketch a Graph| r(t) function | Make a Table of Points

Surface Integral| x,y | x,z | y,z

Position Vectors| Velocity | Acceleration | Speed | Unit Tangent Vector | Parametric Equation | Standard (Linear) Equation

Speed| r(t) function

Sphere| Center Point | Mid Point | Equation | Radius

Surface Area Revolving

Surface Integral| x,y | x,z | y,z

Tangent Plane to a Surface

Trig d/dx – Identities and Functions| Half Angle Formulas | Reciprocals | Integration | Derivatives | 1+cos(2x)2 | 1-cos(2x) / 1+cos(2x) | 1-cos(2x)/2 | cos(2x) | cos(x) | cos²(x) | cot(x) | csc(x) | csc²(x) | sec(x) | sec²(x) | sin(2x) | sin(x) | sin²(x) | sin²(x) + cos²(x) = 1 | tan(x) | tan²(x)

Vectors| Unit Tangent Vector | Unit Vector PQ/||PQ|| | Vector Between P & Q

Velocity

Volume of a Parallelepiped

Work| Force Field | Lifting Object | Pumping Oil

Springs

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