SolveMathAI

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

Worked through step by step. More derivatives.

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

Generated by SolveMath AI and kept here so the next person asking gets it instantly. AI can make mistakes, so check anything that matters.

Solve your own

Same solver, same steps, no account.

Enter to solve · Shift+Enter for a new line

  • Free
  • No account
  • Every step shown
  • Arithmetic to calculus

More solved problems

Derivatives solver →
Find the derivative of x^3 * sin(x)