Explanation Given: The given problem is x 2 + y 3 = 10 Concept Used: d 2 y d x 2 = d d x ( d y d x ) Power rule of differentiation formula d d x x n = n x n − 1 Calculation: To find d 2 y d x 2 where x 2 + y 3 = 10 First, find d y d x by differentiate both side of the equation with respect to x as x 2 + y 3 = 10 d d x [ x 2 + y 3 ] = d d x 10 d x 2 d x + d d x y 3 = 0 2 x + d d x y 3 = 0 power rule 2 x + d d y y 3 d y d x = 0 chain rule 3 y 2 d y d x = − 2 x d y d x = − 2 x 3 y 2 Now, to find d 2 y d x 2 again differentiate both sides of the equation with respect to x, as

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3, Problem 33SP

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To find d2ydx2 for x2+y3=10 .

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Chapter 3, Problem 32SP

Chapter 3, Problem 34SP

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Chapter 3 Solutions

Calculus

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To find d 2 y d x 2 for x 2 + y 3 = 10 .

Solution Summary: The author explains the power rule of differentiation formula dxn=n.

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To find d2ydx2 for x2+y3=10 .

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Chapter 3 Solutions