You are here:

Calculus/differentiate composite funtion using chain rule

Advertisement

Expert: - 3/28/2008


Question
hi.. my name is fiza. i really don't havea any idea how to solve :
4ln(ln(ln(secx)))and tan^3 (cot7x)^1/2 using chain rule.can you help me?

Answer
Remember what the chain rule says: To find the derivative of f(g(x)), it's f'(g(x))*g'(x).  What we have is a very nested chain rule, like
f(g(h(l(x)))) for the first one.

Think of ln(f(t)).  The derivative of the function is f'(t)/ln(f(t)).

Now to find f'(t).  f(t) = ln(g(t)), where g(t) is also ln(t).
The derivative of this is f'(t)=g'(t)/ln(g(t)).

Putting this back into the original gives the derivative is
g'(t)/(ln(f(g(t))ln(g(t)).

When you finally get down to it, the derivative of sec(x) is
sec(x)tan(x).

On exponets of trig functions, the sin^(1.5)(5) can be written as
(sin(5))^(1.5).

For tan^3(cot^(0.5)(7x)), you get
3*tan^2(cot^(0.5)(7x))d(cot^(0.5)(7x))/dx, and d(cot^(0.5)(7x)/dx is
0.5*cot^(-0.5)(7x)*d(cot(7x))/dx.  The derivative of cot(7x) is
-csc^2(7x) d(7x)/dx, and the derivative of 7x is 7.

All you've got to remember is these are extended chain rule and that the derivative of f(g(x)) = f'(g(x))g'(x).  Use this and apply it several times.

Thanks for the question and I hope this will assist you.

Have a great day.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.