Question

D/dx (28000-50x²-400x)

Answer 1

Answer:

  $-100x - 400$

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

  $\dfrac{d}{dx}(28000 - 50x^2 - 400x) = \dfrac{d}{dx}(28000) - \dfrac{d}{dx}(50x^2) - \dfrac{d}{dx}(400x)$

By the constant multiple rule, we have

  $= \dfrac{d}{dx}(28000) - 50\dfrac{d}{dx}(x^2) - 400\dfrac{d}{dx}(x)$

The derivative of any constant is 0.

The power rule says that for any real number $n$, $\frac{d}{dx} x^n = nx^{n-1}$. And note that $x = x^1$. Thus we have

  $= 0 - 50(2)x - 400(1)x^0 = -100x - 400$

since $x^0 = 1$