1007 : The Shortcut

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1007 : The Shortcut. AP CALCULUS. Notation:. The Derivative is notated by:. Newton . L’Hopital. Leibniz. Derivative of the function. With respect to x. Notation used in Cal 3. Notation:. Find the rate of change of the Circumference of a Circle with respect to its Radius. - PowerPoint PPT Presentation

Transcript of 1007 : The Shortcut

AP CALCULUS

1007 : The ShortcutAP CALCULUS

1Notation:The Derivative is notated by:

Newton LHopitalLeibnizDerivative of the functionWith respect to xNotation used in Cal 32Notation:Find the rate of change of the Circumference of a Circle with respect to its Radius.

Find the rate of change of the Area of a Square with respect to the length of a Side.

Find the rate of change of the Volume of a Cylinder with respect to its Height.

A(s)You treat r as a constant3Algebraic RulesREM: A). A Constant Function

0Derivative is the slope of a tangenty = 3m = 004Algebraic RulesB). A Power Function

Rewrite in exponent form!

5

Rewrite in exponent form!Algebraic RulesC). A Constant Multiplier

7Algebraic RulesREM: D). A Polynomial

How do you eat an elephant?One bite at a time8Example: Positive Integer Powers, Multiples, Sums, and Differences

Calculator: [F3] 1: d( differentiateor [2nd ] [ 8 ] d(d(expression,variable)

d( x^4 + 2x^2 - (3/4)x - 19 , x ) 9Do it all !

Step 1: Rewrite using exponentsMust rewrite using exponents!10A conical tank with height of 4 ft is being filled with water.

Write the equation for the volume of the conical tank.

Find the instantaneous rate of change equation of the volume with respect to the radius.

Find the instantaneous rate of change in Volume when the radius is 9 ft.

When the radius is 9 the volume increases 24cu.ft.per minuteSecond and Higher Order Derivatives

functiony y y yiv could be y(4)12Second and Higher Order Derivatives

13Example: Find all the derivatives.

The rest have mathematical uses}14At a Joint PointPiece Wise Defined Functions: The function must be CONTINUOUS Derivative from the LEFT and RIGHT must be equal.

The existence of a derivative indicates a smooth curve; therefore,

Therefore the derivative DNE15Last Update08/12/1016