Find an equation of the tangent line to the curve at the given point.ysin(sin(x)), (2r, 0)

Name: Find an equation of the tangent line to the curve at the given point.
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
Description: Find an equation of the tangent line to the curve at the given point.ysin(sin(x)), (2r, 0)

Answered: Find an equation of the tangent line to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Topic Video

Question

Find an equation of the tangent line to the curve at the given point.
y
sin(sin(x)), (2r, 0)

Expert Solution

Step 1

given function is

$y = \sin (\sin x)$

tangent at point $(2 π, 0)$

derivative of the function,

$\begin{array}{rcl} \frac{d}{d x} y & = & \frac{d}{d x} \sin (\sin x) \\ \frac{d y}{d x} & = & \frac{d \sin (\sin x)}{d \sin x} \frac{d \sin x}{d x} \\ = & \cos (\sin x) \cos x \end{array}$

slope of tangent line will be value of derivative at the point, so

$\begin{array}{rcl} m & = & {(\frac{d y}{d x})}_{x = 2 π} \\ m & = & \cos (\sin 2 π) \cos 2 π \\ = & \cos 0 \\ m & = & 1 \end{array}$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Chain Rule$

Learn more about

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

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated