Test:42 QNo:10

Is (x-1)(x³+x²+x+1)=(x⁴-1) ?

yes sumit

(x-1)(x3+x2+x+1)=(x4-1)

dy / dx = 2

use

\frac{x^4 - 1 }{x- 1} = x^3 + x^2 + x + 1

u get

y = \frac{\left(x- 1 \right)^2}{x^4 - 1}

y .\left(x^4 - 1 \right) = \left(x-1 \right)^2

\frac{dy}{dx} = \frac{2x-2- 4x ^ 3 y }{x ^ 4-1 }

at x =0

\frac{dy}{dx} = \frac{-2 }{-1 } = 2

simply expand by quotients rule and then put X=0