Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Derivative math problem help?
Can't for the life of me figure this one out, think I'm missing something simple. Just need to find first and second derivative of this equation, pretty sure I am using the Power Rule for this one.
f(x) = 2x(2x+1)^5
Thanks for any help you can provide!
2 Answers
- Anonymous7 years ago
2[(2x+1)^5 +5x(2x+1)^4] is the ans u just hav to apply the quotient rule
- MelvynLv 77 years ago
product rule and power rule
u = 2x, v = (2x+1)^5
du/dx = 2 , dv/dx = 5(2x+1)^4 * 2 = 10(2x+1)^4
d(uv)/dx = u dv/dx + v du/dx
= 2x . 10 (2x+1)^4 + (2x+1)^5 . 2 = 20x(2x+1)^4 +2(2x+1)^5
= 2 (2x+1)^4 [ 10x +(2x+1)] = 2 (12x+1)(2x+1)^4
2nd derivative in same way
f'(x) = (2x+1)^4 (24x+2)
u = (2x+1)^4, v = 24x+2
du/dx = 2* 4(2x+1)^3 , dv/dx = 24
d^2f/dx^2 = 24*(2x+1)^4 + 2*4*(24x+2)(2x+1)^3
= 8(2x+1)^3 [3(2x+1) + (24x+2)]
=8(2x+1)^3 [ 30x+5]
=40 (6x+1)(2x+1)^3
