PRODUCT AND QUOTIENT RULES AND HIGHER-ORDER DERIVATIVES

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Product & Quotient Rules Higher Order Derivatives

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Presentation transcript:

PRODUCT AND QUOTIENT RULES AND HIGHER-ORDER DERIVATIVES Section 2.3

When you are done with your homework, you should be able to… Find the derivative of a function using the Product Rule Find the derivative of a function using the Quotient Rule Find the derivative of a trigonometric function Find a higher order derivative of a function

THE PRODUCT RULE The product of two differentiable functions f and g is itself differentiable. The derivative of fg is the first function times the derivative of the second, plus the second function times the derivative of the first.

Find the derivative of

Extension of the Product Rule

Find the derivative of All of the above

THE QUOTIENT RULE The quotient of two differentiable functions f and g is itself differentiable at all values of x for which . The derivative of is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared.

Evaluate and simplify

Evaluate and simplify

Evaluate and simplify

Derivatives of the Remaining Trigonometric Functions

Higher Order Derivatives

Evaluate the third derivative of the function