Explanation Given Information: The provided function is y = x 1 + e 2 x . Formula used: The differentiation of exponential function y = e u with respect to x : d d x e u = e u d u d x Where u is a differentiable function of x . The quotient rule of differentiation: d d x [ u ( x ) v ( x ) ] = v ( x ) d d x u ( x ) − u ( x ) d d x v ( x ) [ v ( x ) ] 2 [ for v ( x ) ≠ 0 ] Where u and v are differentiable functions of x . Calculation: Consider the function provided, y = x 1 + e 2 x Now differentiate both sides with respect to x , d y d x = d d x ( x 1 + e 2 x ) Now apply, quotient rule of differentiation: d d x [ u ( x ) v ( x ) ] = v ( x ) d d x u ( x ) − u ( x ) d d x v ( x ) [ v ( x ) ] 2 To obtain the derivative as: d d x ( x 1 + e 2 x ) = ( 1 + e 2 x ) d d x ( x ) − ( x ) ⋅ d d x ( 1 + e 2 x ) ( 1 + e 2 x ) 2 Now apply, differentiation of exponential function: d d x e u = e u d u d x To obtain the derivative as: ( 1 + e 2 x ) d d x ( x ) − ( x ) ⋅

MATHMATICAL APPLICATIONS FOR THE MANAGEM

11th Edition

ISBN: 9781305758063

Author: HARSHBARGER

Publisher: CENGAGE C

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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.

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Chapter 11.2, Problem 28E

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To calculate: The derivative of function y=x1+e2x.

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Chapter 11.2, Problem 27E

Chapter 11.2, Problem 29E

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Chapter 11 Solutions

MATHMATICAL APPLICATIONS FOR THE MANAGEM

Ch. 11.1 - 1. Ch. 11.1 - 2. If Ch. 11.1 - Prob. 3CP Ch. 11.1 - 4. Find . Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Find the derivatives of the functions in Problems...

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The derivative of function y = x 1 + e 2 x .

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