Differentiate the function. y = e-2" cos 41

Name: Differentiate the function. y = e-2" cos 41
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: Differentiate the function. y = e-2" cos 41

Answered: y = e-2" cos 41

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section: Chapter Questions

Problem 78RE

See similar textbooks

Related questions

Topic Video

Question

Differentiate the function.

Expert Solution

Step 1

Consider the following equation:

$y = e^{- 2 t} \cos (4 t)$

Differentiate $y$ with respect to $t$ :

$\frac{d y}{d t} = \frac{d}{d t} [e^{- 2 t} \cos (4 t)]$

Apply the product rule of differentiation:

$\begin{array}{rcl} \frac{d y}{d t} & = & \cos (4 t) \frac{d}{d t} e^{- 2 t} + e^{- 2 t} \frac{d}{d t} \cos (4 t) \\ = & - 2 e^{- 2 t} \cos (4 t) - 4 e^{- 2 t} \sin (4 t) \\ = & - 2 e^{- 2 t} [\cos (4 t) + 2 \sin (4 t)] \end{array}$

Step by step

Solved in 2 steps

Knowledge Booster

$Rules of Differentiation$

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.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS