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Beliebt Rechnen >

derivative of sqrt(x^4-9x^2+16)

Lösung

\frac{d}{d x} (x^{4} - 9 x^{2} + 16)

Lösung

\frac{x ( 2 x ^{2} - 9 )}{x ^{4} - 9 x ^{2} + 16}

Schritte zur Lösung

\frac{d}{d x} (x^{4} - 9 x^{2} + 16)

Wende die Kettenregel an:

\frac{1}{2 x ^{4} - 9 x ^{2} + 16} \frac{d}{d x} (x^{4} - 9 x^{2} + 16)

= \frac{1}{2 x ^{4} - 9 x ^{2} + 16} \frac{d}{d x} (x^{4} - 9 x^{2} + 16)

\frac{d}{d x} (x^{4} - 9 x^{2} + 16) = 4 x^{3} - 18 x

= \frac{1}{2 x ^{4} - 9 x ^{2} + 16} (4 x^{3} - 18 x)

Vereinfache

\frac{1}{2 x ^{4} - 9 x ^{2} + 16} (4 x^{3} - 18 x) : \frac{x ( 2 x ^{2} - 9 )}{x ^{4} - 9 x ^{2} + 16}

= \frac{x ( 2 x ^{2} - 9 )}{x ^{4} - 9 x ^{2} + 16}

Graph

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