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人気のある微分積分 >

derivative of x^2*{f}(x)

解

\frac{d}{d x} (x^{2} \cdot f (x))

解

2 x f (x) + \frac{d}{d x} (f (x)) x^{2}

解答ステップ

\frac{d}{d x} (x^{2} f (x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = f (x)

= \frac{d}{d x} (x^{2}) f (x) + \frac{d}{d x} (f (x)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

= 2 x f (x) + \frac{d}{d x} (f (x)) x^{2}

人気の例

derivative of e^{-arcsinh(x/2})

\frac{d}{d x} (e^{- arcsinh (\frac{x}{2})})

derivative (sqrt(x))/(6x-6)

d er i v a t i v e \frac{x}{6 x - 6}

derivative of |x|^3

\frac{d}{d x} (∣ x ∣^{3})

integral of 1/(sqrt((4x-x^2)^3))

\int \frac{1}{( 4 x - x ^{2} ) ^{3}} d x

integral of e^{-t(a+s)}

\int e^{- t (a + s)} d t