Explanation Given: The function is f ( u ) = 4 − 3 u . Definition used: The first derivative of the function is the differentiation of the function, f ′ ( u ) = d d u f ( u ) (1) The second derivative of the function is the differentiation of the first derivative of the function, f ″ ( u ) = d d u f ′ ( u ) (2) The chain rule stated that the derivation of the function, f ( g ( x ) ) is f ′ ( g ( x ) ) ⋅ g ′ ( x ) . Formula used: The power rule of the derivatives is, d d x a x n = a ⋅ n ⋅ x n − 1 Calculation: Substitute 4 − 3 u for f ( u ) in equation (1) to find the first derivative of the function, f ′ ( u ) = d d u [ 4 − 3 u ] = 1 2 4 − 3 u ⋅ d d u ( 4 − 3 u ) ( Use chain rule ) = 1 2 4 − 3 u ⋅ ( − 3 ) ( Use power rule ) = − <

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Differential Equations

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Chapter 3.5, Problem 19E

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The first and the second derivative of the function.

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The first and the second derivative of the function.

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