differentiation of a function

Question

Prove dy/dx = sec x for y= ln tan(π/4 + x/2)

Answer 1

This problem can be worked using the chain rule for differentiation.   f(g(x)) = f'(g(x) * g'(x).

 

g(x) = tan(π/4 + x/2)   =>  g'(x) =(1/2) sec²(π/4 + x/2).

 

f'(g(x)) = 1/tan(π/4 + x/2)    do dy/dx =  (1/2)sec²(π/4 + x/2)/tan(π/4 + x/2)

 

Now let's work on some trig identies

sec u = 1/cos u

tan u = sin u/cos u   

 

sec²/tan  =   1/cos * 1/cos * cos/sin = 1/(sin u cos u) =  2/(2sinu cos u) = 2/sin (2u)

 

now let's apply our new identity 

 

dy/dx =  (1/2) * 2/sin [2*(π/4 + x/2)]   = 1/(sin π/2 + x) = 1/(sin π/2 cos x + sin x * cos π/2)

                                                          = 1/(1*cos x + sin x * 0) = 1/cos x = sec x

 

 

Answer 2

If you want help in completing your
1 Assignments
2 Homework
3 Online courses
4 Online Exams
5 Classroom exams

In subjects
1 Finance
2 Statistics
3 Economics
4 Accounting
5 Operations Research
6 Econometric
7 Investments
8 Mathematics
9 Physics
10 Chemistry
11 Probability
12 Business
13 Project Management
14 C programming
15 C++ Programming

Work related to
Minitab
Excel
SPSS
R language

If you have work related to other subjects, I have a bunch of tutors for other subjects at very low prices.

If you wish for live tutoring. I have a separate platform for that at rate 10 dollars per hour.

Perks
1 you can pay me after getting your work done.
2 My fees will be very less as compared to Wyzant and other tutoring sites.

You can contact me through

Facebook search
Wei-Chyung Wang

Mail Id (Gmail account)
[email protected]

Kik messenger

imessage

You can send a message on Wyzant with your details

1 Your name
2 Subject
3 Work details
4 Contact number
5 Mail id

I am running workhelp site since 10 years. I have worked as a professor for 10 years and now with my team working to help students across the globe in their studies. We are working at other sites like chegg tutors as registered tutors.

Payment will be through Paypal.