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emmainna [20.7K]
4 years ago
12

D/dx (28000-50x²-400x)

Mathematics
1 answer:
drek231 [11]4 years ago
8 0

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

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