Explanation Given information: The first given equation is, y = 1 u (1) And the second given equation is, u = x + 1 (2) Formula used: The formula to calculate the differential of a function h ( x ) = [ g ( x ) ] n by General Power Rule is, h ′ ( x ) = n [ g ( x ) ] n − 1 g ′ ( x ) Calculation: Equation (1) is written as, y = u − 1 Differentiate above equation with respect to u on both sides to find the value of d y d u . d y d u = d d u ( u ) − 1 = − 1 ⋅ u − 1 − 1 [ Use General Power Rule and d d x ( x n ) = n x n − 1 , n > 0 ] = − u − 2 = − 1 u 2 Equation (2) is written as, u = x 1 / 2 + 1 Differentiate above equation with respect to x on the both sides to find the value of d u d x . d u d x = d d x [ x 1 / 2 + 1 ] = 1 2 x 1 2 − 1 + 1 &#

10th Edition

ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Chapter 3.3, Problem 54E

To determine

To find: The value of dydu , dudx and dydx .

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Chapter 3.3, Problem 53E

Chapter 3.3, Problem 55E

Chapter 3 Solutions

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Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The value of d y d u , d u d x and d y d x .

Solution Summary: The author explains the formula used to calculate the differential of a function h(x)= left[gsqrt]n.

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To find: The value of dydu , dudx and dydx .

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Chapter 3 Solutions