Source: Extra Practice

Find the derivative of f(x)=x3−2x+10f(x) = x^3 - 2x + 10 with respect to xx.

Options

Option A

3x2−2+103x^2 - 2 + 10

Option B is correct

3x2−23x^2 - 2

Option C

x2−2x^2 - 2

Option D

3x2−x3x^2 - x

Explanation

Using the power rule d/dx(x^n) = nx^(n-1) and the rule that the derivative of a constant is 0: d/dx(x^3) = 3x^2, d/dx(-2x) = -2, and d/dx(10) = 0. Adding these gives 3x^2 - 2. Option A incorrectly kept the constant 10. Option C used the wrong coefficient for x^2. Option D incorrectly differentiated -2x.