SOLUTION: Greetings math tutors, Find dy/dx for y=(x^2-1)(3x+2)^2 and for y=cos(1/4πx). Thanks in advance from Ireland, -AMH

Algebra ->  Rational-functions -> SOLUTION: Greetings math tutors, Find dy/dx for y=(x^2-1)(3x+2)^2 and for y=cos(1/4πx). Thanks in advance from Ireland, -AMH      Log On


   

Question 870678: Greetings math tutors,
Find dy/dx for y=(x^2-1)(3x+2)^2 and for y=cos(1/4πx).
Thanks in advance from Ireland,
-AMH
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the chain rule.
dy%2Fdx=%28x%5E2-1%29%2A2%283x%2B2%29%2A3%2B%283x%2B2%29%5E2%282x-1%29
dy%2Fdx=%283x%2B2%29%286x%5E2-6%2B%283x%2B2%29%282x%29%29
dy%2Fdx=%283x%2B2%29%286x%5E2-6%2B%286x%5E2%2B4x%29%29
dy%2Fdx=%283x%2B2%29%2812x%5E2%2B4x-6%29
dy%2Fdx=2%283x%2B2%29%286x%5E2%2B2x-3%29
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dy%2Fdx=-sin%28%28pi%2Ax%29%2F4%29%2A%28pi%2F4%29
dy%2Fdx=-%28pi%2F4%29%2Asin%28%28pi%2F4%29%2Ax%29%29

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1) let f(x) = (x^2 - 1) and g(x) = (3x + 2)^2, then
(dy/dx)[f(x)g(x)] = f(x)g'(x) + g(x)f'(x)
f'(x) = 2x and g'(x) = 2(3x+2)
(dy/dx)[f(x)g(x)] = (x^2 - 1)*2(3x+2) + (3x+2)^2 * 2x
(dy/dx)[f(x)g(x)] = 6x^3-6x+4x^2-4 + 9x^2+12x+4
(dy/dx)[f(x)g(x)] = 6x^3 + 13x^2 +6x
2) let f(x) = cos(1/4πx)
(dy/dx)[f(x)] = -(π/4)sin(1/4πx)