Find the derivative. Simplify where possible.y =coth - 1 ( sec x)

Name: Find the derivative. Simplify where possible.y =coth - 1 ( sec x)
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
Description: Find the derivative. Simplify where possible.y =coth - 1 ( sec x)

Answered: Find the derivative. Simplify where…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

See similar textbooks

Related questions

Topic Video

Question

Find the derivative. Simplify where possible.

y =coth ^-¹( sec x)

Expert Solution

Step 1

We have to differentiate the function:

$y = c o t h^{- 1} (s e c x)$

We know the formula of differentiation,

$\begin{array}{rcl} \frac{d c o t h^{- 1} x}{d x} & = & \frac{1}{1 - x^{2}} \\ \frac{d s e c x}{d x} & = & s e c x \tan x \end{array}$

Differentiating the function with respect to $' x'$ , we get

$\begin{array}{rcl} \frac{d y}{d x} & = & \frac{d c o t h^{- 1} (s e c x)}{d x} \\ = & \frac{1}{1 - s e c^{2} x} \frac{d s e c x}{d x} \\ = & \frac{1}{- (s e c^{2} x - 1)} (s e c x \tan x) \end{array}$

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

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, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Find the derivative. Simplify where possible. y =coth - 1 ( sec x)