   Chapter 2.R, Problem 25E

Chapter
Section
Textbook Problem

# 13–40 Calculate y ' . y = sec 2 θ 1 + 2 tan θ

To determine

To calculate:

y'

Explanation

Rule:

i. Sum rule:

ddxfx+g(x)=ddxfx+ddxgx

ii. Chain rule:

dydx=dydu.dudx

iii.

ddθ(secθ)=secθ.tanθ

iv.

ddθ(tanθ) =sec2θ

v. Quotient rule:

ddxuv=u'v-v'uv2

vi. Power rule:

ddxxn=nxn-1

vii. Constant multiple rule:

ddxcfx=c.ddxfx

viii.

1+tan2x=sec2x   tan2x-sec2x = -1

Given:

y=sec2θ1+tan2θ

Calculation:

y=sec2θ1+tan2θ

Differentiate with respect to θ

y'=ddθsec2θ1+tan2θ

By using quotient rule

y'=1+tan2θddθsec2θ- sec2θ.ddθ1+tan2θ 1+ tan2θ2

By using rule ddθ(secθ)=secθ.tanθ, chain rule and sum rule

y'=1+tan2θsec2θ.tan2θ. ddθ(2θ)- sec2θ.(ddθ(1)+ddθtan2θ) 1+ tan2θ2

By using power rule and constant multiple rule

y'=1+tan2θsec2θ

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Evaluate the integral. 17. xx27dx

Single Variable Calculus: Early Transcendentals

#### The implied domain of is: (1, ∞) (−∞, 1) x ≠ 1 (−1, 1)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### In Exercises 116, determine whether the argument is valid. pq~pq

Finite Mathematics for the Managerial, Life, and Social Sciences 