derivative (4x^2-7)^{1/2}

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d t} (8000 (1.12)^{t})

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d er i v a t i v e \frac{1500}{x}