Explanation Given Information: The function is y ( x ) = cos ( e x ) + e x cos x . Formula Used: The chain rule is used which can be represented with the following formula: d d x ( cos u ) = d d x ( cos u ) ⋅ d u d x The product rule is used which can be represented with the following formula: d d x ( x ⋅ y ) = d d x ( x ) ⋅ y + x ⋅ d y d x The following derivative formulas are used: d d x ( cos x ) = − sin x d d x ( e x ) = e x Calculation: Consider the function y ( x ) = cos ( e x ) + e x cos x . Represent the function in the form of d y d x . d d x [ cos ( e x ) + e x cos x ] Separate the terms of the derivative of function. d d x [ cos ( e x ) ] + d d x [ e x cos x ] Then consider the first expression d d x [ cos ( e x ) ]

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 16.2, Problem 29E

To determine

To calculate: The derivative of y(x)=cos(ex)+excosx.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.2, Problem 28E

Chapter 16.2, Problem 30E

Students have asked these similar questions

A ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.) (a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt= feet/sec. (b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt= feet/sec.

Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later? Step 1 Using the diagram of a right triangle given below, the relation between x, y, and z is z² = x²+ +12 x Step 2 We must find dz/dt. Differentiating both sides and simplifying gives us the following. 2z dz dt dx 2x. +2y dt dx dy dz x +y dt dt dt 2z dy dt × dx (x+y dt dy dt

An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters. 9 ground level Assume that x is increasing at a rate of 3 meters/sec. (a) Write as a function of x: 0= (b) When x=10, the angle is changing at a rate of rad/sec. (c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R? ○ Yes ○ No

Chapter 16 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The derivative of y ( x ) = cos ( e x ) + e x cos x .

Solution Summary: The author explains how to calculate the derivative of y(x)=mathrmcos

Videos

To calculate: The derivative of y(x)=cos(ex)+excosx.

Want to see the full answer?

Chapter 16 Solutions