Explanation Proof: If n is any real number then power rule of differentiation is, d d x ( x n ) = n x n − 1 Let the function f be f ( x ) = x 3 . Use the definition of differentiation to find the derivative of the function f ( x ) = x 3 . f ′ ( x ) = d d x f ( x ) = lim h → 0 f ( x + h ) − f ( x ) h = lim h → 0 ( x + h ) 3 − ( x ) 3 h = lim h → 0 ( x 3 + 3 x 2 h + 3 x h 2 + h 3 ) − ( x ) 3 h [ Use ( x + y ) 3 = x 3 + 3 x 2 y + 3 x y 2 + y 3 ] Simplify it further

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ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Chapter 3.1, Problem 78E

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To prove: The power rule of differentiation for n=3 .

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To prove: The power rule of differentiation for n = 3 .

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Chapter 3 Solutions