Explanation Given: The function, y = x + 1 x 3 + x − 2 . Concept Used: The quotient rule of derivatives: d d x [ f ( x ) g ( x ) ] = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) ( g ( x ) ) 2 Power rule of derivatives: d d x ( x n ) = n x n − 1 d d x ( e x ) = e x Calculation: In order to find the derivative of the given function, use the quotient rule of derivatives. Observe that the given function is a quotient of two functions x + 1 and ( x 3 + x − 2 ) . So, using the quotient rule and power rule of derivatives, it gives y ' = d d x ( x + 1 x 3 + x − 2 ) = ( x 3 + x − 2 ) ⋅ d d x ( x + 1 ) − ( x + 1 ) ⋅ d d x ( x 3 + x − 2 ) ( x 3 + x − 2

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 3.4, Problem 18E

To determine

The derivative of the function, y=x+1x3+x−2 .

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Chapter 3.4, Problem 17E

Chapter 3.4, Problem 19E

Chapter 3 Solutions

Biocalculus

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The derivative of the function, y = x + 1 x 3 + x − 2 .

Solution Summary: The author explains how to find the derivative of the given function using the quotient rule of derivatives.

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The derivative of the function, y=x+1x3+x−2 .

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Chapter 3 Solutions