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Derivatives

Power, product, quotient and chain rules, applied one at a time.

The derivative is the slope of the graph at each point. It is computed by rules — power, sum, constant multiple, product, quotient, chain — and the solver applies exactly one rule per step so you can see which rule fires where. The dashed curve is the derivative plotted against the function.

작업 예제: derivative of sin(x)*x^2

Calculus · Derivatives

Differentiate x^2·sin(x)

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

단계별로

  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.

답을 드러내세요
f'(x) = x \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)

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