what is the derivative of (1-x)^6(x^2+7)^8?

Question

what is the derivative of (1-x)^6(x^2+7)^8

is it y=(1-x)^5(x^2+7)^7(-8x^2+3x-42) ??

I'm not sure

Answer 1

(-6)(1 - x)^5(x² + 7)^8 + 8(x² + 7)^(7)(2x)(1 - x)^(6)
2[(- 3)(1 - x)^5(x² + 7)^7 { (x² + 7) + 8x(1 - x) } ]
2 [ (- 3)(1 - x)^5 (x² + 7)^7 (7 + 8x - 7x²) ]
(- 6) (1 - x)^5 (x² + 7)^7 (7 + 8x - 7x²)
Not a good question for typing---may have slipped up somewhere!

Answer 2

Product rule:
(uv)' = u'v + uv'

u = (1-x)^6
u' = -6(1-x)^5

v = (x^2 + 7)^8
v' = 16x(x^2 + 7)^7

(uv)'
= [-6(1-x)^5 * (x^2 + 7)^8] + [(1-x)^6 * 16x(x^2 + 7)^7]
= [(1-x)^5][(x^2+7)^7][-6(x^2 + 7) + 16x(1-x)]
= [(1-x)^5][(x^2+7)^7][-6x^2 - 42 + 16x - 16x^2]
= [(1-x)^5][(x^2+7)^7][-22x^2 + 16x - 42]

Answer 3

(1-x)^6 * 8(x^2+7)(2x) + 6(1-x)^5 * (x^2+7)^8


apply product rule and chain rule

Answer 4

= [6(1-X)^5 * 6(x^2+7)^8] + [(1-x)^6 * 48(x^2+7)^7 * 2]
=[30 * (1-X)^5 * (x^2+7)^8] + [96 * (1-x)^6 * (x^2+7)^7]

Luego sacas factor común
= [(1-X)^5 * (x^2+7)^] * [30 (x^2+7)+ 96 (1-x)]
Si la puedes reducir más lo haces y listo.

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