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Calculus · Derivatives

Differentiate x^2y^4

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

Step by step

  1. \frac{d}{dy}\left[x^{2} y^{4}\right]

    Differentiate 2 times, one derivative at a time.

  2. x^{2} \frac{d}{d y} y^{4}

    Constant multiple rule: pull the constant out.

  3. 4 x^{2} y^{3}

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

  4. f^{(1)}(y) = 4 x^{2} y^{3}

    That is derivative number 1.

  5. 4 x^{2} \frac{d}{d y} y^{3}

    Constant multiple rule: pull the constant out.

  6. 12 x^{2} y^{2}

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

  7. f^{(2)}(y) = 12 x^{2} y^{2}

    That is derivative number 2.

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