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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(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

Vereinfache

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

Graph

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