Answer:
[tex]-100x - 400[/tex]
Step-by-step explanation:
The derivative of a sum is the sum of the derivatives by the sum rule, and this also extends to differences by the constant multiple rule
[tex]\dfrac{d}{dx}(28000 - 50x^2 - 400x) = \dfrac{d}{dx}(28000) - \dfrac{d}{dx}(50x^2) - \dfrac{d}{dx}(400x)[/tex]
By the constant multiple rule, we have
[tex]= \dfrac{d}{dx}(28000) - 50\dfrac{d}{dx}(x^2) - 400\dfrac{d}{dx}(x)[/tex]
The derivative of any constant is 0.
The power rule says that for any real number [tex]n[/tex], [tex]\frac{d}{dx} x^n = nx^{n-1}[/tex]. And note that [tex]x = x^1[/tex]. Thus we have
[tex]= 0 - 50(2)x - 400(1)x^0 = -100x - 400[/tex]
since [tex]x^0 = 1[/tex]
