Lesson 2.3 Product & Quotient Rules and Higher Derivatives.

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Presentation transcript:

Lesson 2.3 Product & Quotient Rules and Higher Derivatives

Product Rule If a function is the product of 2 functions, the derivative is: 1 st ● (derivative of 2 nd ) + 2 nd ● (derivative of 1 st )

Example

Quotient Rule If a function is the quotient of 2 functions, the derivative is: [bottom ● (derivative of top) − top ● (derivative of bottom)] ÷ bottom 2

Mathematical Proofs: The Product Rule

Example

More Trig Derivatives

Draw the position of a ball rolling off a table: Now try to draw a graph of the velocity of the ball:

Finally, graph the acceleration of the ball:

Higher Order Derivatives s(t)position v(t) = s’(t)velocity a(t) = v’(t) = s’’(t)acceleration

Example Problem Set 2.3