derivative f(x)=sqrt(1+x^{256)}-1

解答

导数

f (x) = 1 + x^{256} - 1

\frac{128 x ^{255}}{x ^{256} + 1}

求解步骤

\frac{d}{d x} (1 + x^{256} - 1)

使用微分加减法定则:

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

= \frac{d}{d x} (1 + x^{256}) - \frac{d}{d x} (1)

\frac{d}{d x} (1 + x^{256}) = \frac{128 x ^{255}}{1 + x ^{256}}

\frac{d}{d x} (1) = 0

= \frac{128 x ^{255}}{1 + x ^{256}} - 0

化简

= \frac{128 x ^{255}}{x ^{256} + 1}

\frac{d}{d x} (2 x 36 - x^{2})

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