derivatives

Question

Find  dy/dx for the following functions    Y = 10(x + 1)(4 - x)

Answer 1

Given function y = 10(x+1)(4-x)

y = (10x+10)(4-x)

y = 40x-10x^2+40-10x

y = -10x^2+30x+40

Apply derivative to each side with respect of x.

dy/dx = d/dx(-10x^2+30x+40)

Remeber the formula d/dx (x^n) = nx^n-1

d/dx (x) = 1

d/dx(constant) = 0

dy/dx = d/dx(-10x^2)+d/dx(30x)+d/dx(40)

= -10*2x+30+0

= -20x+30

Derivative of y is -20x+30.