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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.

Ví dụ đã làm: derivative of sin(x)*x^2

Calculus · Derivatives

Differentiate x^2·sin(x)

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

Bước một bước

  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.

Giải đáp
f'(x) = x \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)

Thử đi.

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