You are here:
Calculus/Calc 160
Advertisement
Question
im asked to differentiate y=(5x-5)^3(3-x^4)
after using the chain rule and product rule i get
(5x-5)^3(-12x^3(3-x^4)^2)+(3-x^4)^3(15(5x-5)^2
but i am completely lost on how to factor this down
Let f(x) = (5x-5)^3 and g(x) = 3-x^4;
The result would be y' = fg' + gf'.
Now f'(x) = 15(5x-5)^2 and g'(x) = -4x^3.
From what the answer you have looks like, we should really have
Let f(x) = (5x-5)^3 and g(x) = (3-x^4)^3;
Still, the result would be y' = fg' + gf'.
Now f'(x) = 15(5x-5)^2 and g'(x) = -12(3-x^4)^2.
In this case, the answer of y' = fg' + gf' has a factor of
[(5x-2)^2][(3-x^4)^2] that can be taken out of both terms.
This will leave [(5x-2)^2][(3-4x^4)^2][(5x-5)(3-x^4) + 15(3-x^4)].
The inside of the parenthesis can be multiplied out, but I don't know if anything factors out os that, but it will start, when ordered by power, with -5x^5.
Related Articles
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.