derivative f(x)=(8x-7)^{1/2}

Lösung

ableitung von

f (x) = (8 x - 7)^{\frac{1}{2}}

\frac{4}{( 8 x - 7 ) ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{d}{d x} ((8 x - 7)^{\frac{1}{2}})

Wende die Kettenregel an:

\frac{1}{2 ( 8 x - 7 ) ^{\frac{1}{2}}} \frac{d}{d x} (8 x - 7)

= \frac{1}{2 ( 8 x - 7 ) ^{\frac{1}{2}}} \frac{d}{d x} (8 x - 7)

\frac{d}{d x} (8 x - 7) = 8

= \frac{1}{2 ( 8 x - 7 ) ^{\frac{1}{2}}} \cdot 8

Vereinfache

\frac{1}{2 ( 8 x - 7 ) ^{\frac{1}{2}}} \cdot 8 : \frac{4}{( 8 x - 7 ) ^{\frac{1}{2}}}

= \frac{4}{( 8 x - 7 ) ^{\frac{1}{2}}}

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