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Find the derivative of x^4 - 3x^2 + 7

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Answer
4x3−6x\boxed{4x^3 - 6x}

Substituting a test value like x=1x=1 into the derivative yields −2-2, which correctly matches the instantaneous rate of change of the original polynomial at that point.

Problem: Find the derivative of f(x)=x4−3x2+7f(x) = x^4 - 3x^2 + 7.

Steps

  1. Apply the sum and difference rule
    ddx(x4)−ddx(3x2)+ddx(7)\frac{d}{dx}(x^4) - \frac{d}{dx}(3x^2) + \frac{d}{dx}(7)
  2. Apply the power rule and constant rule
    4x3−3(2x)+04x^3 - 3(2x) + 0
  3. Simplify the expression
    4x3−6x4x^3 - 6x

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