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lecture11 - Section 3.2 Derivative Rules Powers Multiples...

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Section 3.2: Derivative Rules Powers, Multiples, Sums, Differences 1. Derivative of a Constant Function If f ( x ) = c for a constant c then Proof: 2. Power Rule If n is any real number, then for all x where the powers x n , x n - 1 are defined. 1

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Example: Find the derivatives of f ( x ) = x, g ( x ) = x, h ( x ) = x 3 , k ( x ) = x 2+ π 3. Constant Multiple Rule If u is a differentiable function of x , and c is a constant, then Examples Find d dx (3 x 2 ) , d dx ( - u ) 2
4. Derivative Sum and Difference Rules If u, v are both differentiable functions with respect to x , then at every point where both u and v are differentiable. Example Find y ( x ) where y = x 3 + 4 3 x 2 - 5 x + 1 Derivative of the Natural Exponential Function From the definition of a derivative, we have that d dx e x = lim h 0 3

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Products and Quotients
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lecture11 - Section 3.2 Derivative Rules Powers Multiples...

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