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Calculus · Derivatives

Differentiate x^4

\frac{d^2}{dx^2}\left[x^{4}\right]

Step by step

  1. \frac{d}{dx}\left[x^{4}\right]

    Differentiate 2 times, one derivative at a time.

  2. 4 x^{3}

    Power rule: (xⁿ)′ = n·xⁿ⁻¹ with n = 4.

  3. f^{(1)}(x) = 4 x^{3}

    That is derivative number 1.

  4. 4 \frac{d}{d x} x^{3}

    Constant multiple rule: pull the constant out.

  5. 12 x^{2}

    Power rule: (xⁿ)′ = n·xⁿ⁻¹ with n = 3.

  6. f^{(2)}(x) = 12 x^{2}

    That is derivative number 2.

Reveal the answer
f''(x) = 12 x^{2}