CALCULUS: Differentiate y = -11x^4 + 2x^3 - 4x^2 + 2x - 7? (Using rules for finding the derivative) 10 points for the answer with solution.?

Come after 50 minutes and chose best answer
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Rules used here:
d(u + v)/dx = d(u)/dx + d(v)/dx
d(x^n)/dx = nx^(n-1)
d(n)/dx = 0 ; Given that n is a constant here

y = -11x^4 + 2x^3 - 4x^2 + 2x - 7

Differentiate with respect to x
dy/dx = d(-11x^4 + 2x^3 - 4x^2 + 2x - 7)/dx

= -d(11x^4)/dx + d(2x^3)/dx - d(4x^2)/dx + d(2x)/dx - d(7)/dx

= -11d(x^4)/dx + 2d(x^3)/dx - 4d(x^2)/dx + 2d(x)/dx - 0

= -44x^3 + 6x^2 - 8x + 2 (Answer)

Rules :
(d/dx)[f(x) + g(x)] = (d/dx)f(x) + (d/x)g(x)
(d/dx)ax^n = a (d/dx)x^n
(d/dx)x^n = nx^(n - 1)
(d/dx)a = 0
*where a and n are constant.

y = -11x^4 + 2x^3 - 4x^2 + 2x - 7

(d/dx)y
= (d/dx)(-11x^4 + 2x^3 - 4x^2 + 2x - 7)
= -11(d/dx)( x^4) + 2(d/dx)(x^3) - 4(d/dx)(x^2) + 2(d/dx)(x) - (d/dx)(7)
= -11(4x^3) + 2(3x^2) - 4(2x) + 2(1) - 0
= -44x^3 + 6x^2 - 8x + 2

y = -11x^4+2x^3-4x^2+2x-7

Using the rule d/dx (x^n) = n x^(n-1)

y' = -11 (4x^3) + 2 (3x^2) - 4 (2x) + 2 (1)
y' = -44x^3 +6x^2 -8x +2

dy/dx = - 44x^3 + 6x^2 - 8x + 2