Question

D/dx (28000-50x²-400x)

Answer 1

`-100x - 400`

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

`(d)/(dx)(28000 - 50x^2 - 400x) = (d)/(dx)(28000) - (d)/(dx)(50x^2) - (d)/(dx)(400x)`

By the constant multiple rule, we have

`= (d)/(dx)(28000) - 50(d)/(dx)(x^2) - 400(d)/(dx)(x)`

The derivative of any constant is 0.

The power rule says that for any real number
`n`,
`(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`