Question

найти производную функции (4-x)(x-1)(4+x)(x+1)​

Answer 1

(4-x)(x-1)(4+x)(x+1) = (4²-x²)(x²-1²) = (16 - x²)(x² - 1) = -x⁴ + 17x² - 16

((4-x)(x-1)(4+x)(x+1))' = (-x⁴ + 17x² - 16)' = (-x⁴)' + (17x²)' - (16)' = -(x⁴)' + 17(x²)' - 0 = -4x³ + 34x

Ответ: -4x³ + 34x

Answer 2

Ответ:

$y=(4-x)(x-1)(4+x)(x+1)\ \ \Rightarrow \ \ \ y=(16-x^2)(x^2-1)\\\\\\\boxed{(uv)'=u'v+uv'\ \ ,\ \ (x^{n})'=n\cdot x^{n-1\ }}\\\\\\y'=-2x\, (x^2-1)+2x\, (16-x^2)=-2x^3+2x+32x-2x^3=-4x^3+34x$