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Unformatted text preview: MATH1010U: Chapter 3 1 DIFFERENTIATION RULES Derivatives of Polynomials and Exponential Functions(3.1,p183) Recall: Last day, we learned how to find the derivative from first principles. Now, let’s consider some useful rules to help us do differentiation. Derivative of a Constant Function: ) ( = c dx d The Power Rule (General Version): If n is any real number, then 1 ) ( − = n n x n x dx d The Constant Multiple Rule: If c is a constant and f is a differentiable function, then ) ( )) ( ( x f dx d c x f c dx d ⋅ = ⋅ The Sum Rule: If f and g are both differentiable, then [ ] ) ( ) ( ) ( ) ( x g dx d x f dx d x g x f dx d + = + The Difference Rule: If f and g are both differentiable, then [ ] ) ( ) ( ) ( ) ( x g dx d x f dx d x g x f dx d − = − Now that we know how to differentiate polynomials, let’s consider some other functions, e.g. the exponential function. Exponential Function Recall: Earlier in the course, we introduced the exponential function. MATH1010U: Chapter 3 2 Question:...
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