Explanation Given: The given equation is y = ( 1 − x ) x and the point is x = 0 . Concept Used: Product rule of differentiation formula d d x ( u v ) = v d d x u + u d d x v Chain rule of differentiation is: d d x f [ g ( x ) ] = d d g f ( g ) d g d x , where u is a differentiable function at x and f is a differentiable function at u ( x ) To find an equation of the tangent line to the graph of an equation y = f ( x ) at the a point ( a , b ) First find slope of the equation at the prescribed point as: m = d y d x | ( a , b ) Now, the equation of the tangent line to the graph of the equation is y = m x + c Put ( a , b ) coordinate in y = m x + c to find the value of c Calculation: To find an equation of the tangent line to the graph of y = ( 1 − x ) x where x = 0 First find slope of the equation at the prescribed point as: m = d y d x | ( a , b ) To differentiate this equation, first take log both side of the equation, as log y = log ( 1 − x ) x log y = x log ( 1 − x ) Now, differentiate both side of the equation with respect to x as log y = x log ( 1 − x ) d d x ( log y ) = d d x ( x log ( 1 − x ) ) d d y ( log y ) d y d x

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

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

Publisher: Kendall Hunt Publishing

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Chapter 3, Problem 44SP

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To find an equation of the tangent line to the graph of given equation y=(1−x)x at the point x=0 .

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Chapter 3, Problem 43SP

Chapter 3, Problem 45SP

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Chapter 3 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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To find an equation of the tangent line to the graph of given equation y = ( 1 − x ) x at the point x = 0 .

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To find an equation of the tangent line to the graph of given equation y=(1−x)x at the point x=0 .

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Chapter 3 Solutions