Explanation Given information: The given function is f ( t ) = ( t − 1 − t − 2 ) 3 . Formula used: For the derivative of addition or subtraction of two functions, sum or difference rule is, h ( x ) = [ f ( x ) ± g ( x ) ] h ′ ( x ) = [ d d x f ( x ) ] ± [ d d x g ( x ) ] If the function f is differentiable and h ( x ) = [ f ( x ) ] n ( n , a real number ) , then chain rule for power function is, h ′ ( x ) = d d x [ f ( x ) ] n = n [ f ( x ) ] n − 1 f ′ ( x ) Calculation: Use the formula of chain rule of differentiation for power function to evaluate the derivative of f ( t ) . f ′ ( t ) = [ 3 ( t − 1 − t − 2 ) 3 − 1 d d t ( t − 1 − t − 2 ) ] <

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ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Chapter 3.3, Problem 25E

To determine

The derivative of the given function.

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Chapter 3.3, Problem 24E

Chapter 3.3, Problem 26E

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The derivative of the given function.

Solution Summary: The author explains the derivative of the given function, which is f(t)3, and the chain rule of differentiation for power function.

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