Sec. 3.3: Rules of Differentiation. The following rules allow you to find derivatives without the direct use of the limit definition. The Constant Rule.

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Presentation transcript:

Sec. 3.3: Rules of Differentiation

The following rules allow you to find derivatives without the direct use of the limit definition. The Constant Rule

Sec. 3.3: Rules of Differentiation The Constant Rule

Sec. 3.3: Rules of Differentiation Ex:y = 4 Ex: Ex:y = e y' = 0 f '(x) = 0 y' = 0 The Constant Rule

Sec. 3.3: Rules of Differentiation The Power Rule

Sec. 3.3: Rules of Differentiation Ex:y = x 4 Ex: y ' = 4x 3 The Power Rule

Sec. 3.3: Rules of Differentiation Ex: Find the slope of the graph of when x = 4. The Power Rule

Sec. 3.3: Rules of Differentiation Ex: Find the equation of the tangent line to f (x) = x 3 when x = –3. The Power Rule In order to write the equation of the tangent line, we need a point on the line. Use point-slope form to write the equation:

Sec. 3.3: Rules of Differentiation The Constant Multiple Rule

Sec. 3.3: Rules of Differentiation The Sum and Difference Rule

Sec. 3.3: Rules of Differentiation Derivatives of Sine and Cosine Functions