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Calculus · Derivatives

Differentiate x^2·sin(x)

\frac{d}{dx}\left[x^{2} \sin{\left(x \right)}\right]

Step by step

  1. \frac{d}{dx}\left[x^{2} \sin{\left(x \right)}\right]

    Start from the derivative to compute.

  2. x^{2} \frac{d}{d x} \sin{\left(x \right)} + \sin{\left(x \right)} \frac{d}{d x} x^{2}

    Product rule with u = x^{2} and v = \sin{\left(x \right)}: (uv)′ = u′v + uv′.

  3. x^{2} \cos{\left(x \right)} + \sin{\left(x \right)} \frac{d}{d x} x^{2}

    (sin u)′ = cos u.

  4. x^{2} \cos{\left(x \right)} + 2 x \sin{\left(x \right)}

    Power rule: (xⁿ)′ = n·xⁿ⁻¹ with n = 2.

  5. x \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)

    Simplify.

Reveal the answer
f'(x) = x \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)