Find the derivative of f(x) = x^3 - 2x + 10 with respect to x.
Model Answer & Options
Source: Extra Practice3x^2 - 2 + 10
3x^2 - 2
x^2 - 2
3x^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.
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