(a) Explanation The given equation is x y = 1 . Simplify the given equation in terms of in terms of x , ( x y ) = 1 x y x = 1 x ( Divide by x in each side ) y = 1 x Differentiate above equation with respect to x and simplify, d d x ( y ) = d d x ( 1 x ) d y d x = d d x ( x − 1 ) ( ∵ 1 (b) To determine To find: The derivative d y d x of the given implicit equation for y in terms of x and examine the derivative values are equivalent.

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ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Chapter 3.6, Problem 3E

(a)

To determine

To find: The derivative dydx of the equation xy=1 explicitly for y in terms of x.

(b)

To determine

To find: The derivative dydx of the given implicit equation for y in terms of x and examine the derivative values are equivalent.

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Chapter 3.6, Problem 2E

Chapter 3.6, Problem 4E

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Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

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Does the series converge or diverge

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The derivative d y d x of the equation x y = 1 explicitly for y in terms of x .

Solution Summary: The author explains how to find the derivative of the equation xy=1 explicitly for y in terms of X.

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To find: The derivative dydx of the equation xy=1 explicitly for y in terms of x.

To find: The derivative dydx of the given implicit equation for y in terms of x and examine the derivative values are equivalent.

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Chapter 3 Solutions