You are here:
- Home
- Teens
- Homework/Study Tips
- Calculus
- Calculus Finding derivative
Calculus/Calculus Finding derivative
Advertisement
Question
If y = x^(x^3) for x > 0, then find dy/dx
This is almost like a product rule, except that it is an exponential problem. Read slow and understand.
The derivative of f(x)^g(x) is like looking at f(x)^n and m^g(x).
Here, f(x) = x and g(x) = x^3.
In the first one, n is really g(x).
In the second one, m is really f(x).
The two parts of the derivative would be
[nf(x)^(n-1)]f'(x) + [m^g(x)]ln(m)g'(x).
If we put back in what n amd m are, we get
[g(x)f(x)^(g(x)-1)]f'(x) + [f(x)^g(x)]g'(x)ln(f(x)).
In the write order it would be
g(x)f'(x)f(x)^(g(x)-1) + ln(f(x))g'(x)f(x)^g(x).
Basically, anyway you have two functions, treat them each individually when taking the derivative.
It may take a few minutes to read the problem and understand.
I could always explain it furtheer.
Related Articles
- Ideal Gas Example Problem - Unknown Gas - Worked Chemistry Problems
- Sample Chemistry Problems - Mass Relations in Balanced Equations
- Mass Relations in Balanced Equations Example Problem - Finding Mass of Reagents and Products
- Toshiba Qosmio G15
- NHL Free Agents in 2009 - A List of Unrestricted NHL Free Agents Available in the Summer of 2009
Answers by Expert:
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.