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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.

काम में एक अच्छी मिसाल: derivative of sin(x)*x^2

Calculus · Derivatives

Differentiate x^2·sin(x)

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

चरण द्वारा कदम

  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.

जवाब दिखाएँ
f'(x) = x \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)

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अधिक में Calculus

LimitsIntegralsDefinite integralsTaylor seriesSeries and sumsMaxima and minima