derivative (x^4+2x^2)/(x^2)

解答

导数

\frac{x ^{4} + 2 x ^{2}}{x ^{2}}

2 x

求解步骤

\frac{d}{d x} (\frac{x ^{4} + 2 x ^{2}}{x ^{2}})

化简

\frac{x ^{4} + 2 x ^{2}}{x ^{2}} : x^{2} + 2

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

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (2) = 0

= 2 x + 0

化简

= 2 x

\int e^{x} (x^{2} - 5 x) d x

\frac{d y}{d x} = \frac{x ^{3}}{y ^{2}}

\int (1 - cos (2 x))^{2} d x

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