find dy/dx of y = (8x - 1)(x^2 +4x +7)(x^3 - 5)
2006-12-30 15:29:23 · 2 answers · asked by DaOne 1 in Science & Mathematics ➔ Mathematics
You either use the "extended" product rule:
dy/dx=8(x^2+4x+7) (x^3-5)+(8x-1) (2x+4)(x^3-5)+ (8x-1)(x^2+4x+7) (3x^2)
or you distribute first y= 8*x^6-47*x^3+ 31*x^5-155*x^2 +52*x^4-260*x+ 35 then just use the power rule dy/dx= 48x^5-141x^2 + 155x^4-310x + 204x^3-260.
Which one is preferable? It depends on where you are going with the problem! If it is just a Mickey Mouse show me you know the theorems problem, then option #1 is the thing to do. If you want to find local extrema, you will need to solve for when y'=0 and that means you either distribute out the expression for y' or option #2 distribute first then differentiate. So option #2 is better for problem #2..........
2006-12-30 17:13:48 · answer #1 · answered by a_math_guy 5 · 0⤊ 0⤋
y=8(2x+4)(3x^2)
2006-12-31 00:07:06 · answer #2 · answered by Tan L 2 · 0⤊ 1⤋