derivative y=sqrt(7x^3-6x^2-8/x)

Lösung

ableitung von

y = 7 x^{3} - 6 x^{2} - \frac{8}{x}

\frac{21 x ^{4} - 12 x ^{3} + 8}{2 x ^{\frac{3}{2}} 7 x ^{4} - 6 x ^{3} - 8}

Schritte zur Lösung

\frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x})

Wende die Kettenregel an:

\frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} \frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x})

= \frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} \frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x})

\frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x}) = 21 x^{2} - 12 x + \frac{8}{x ^{2}}

= \frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} (21 x^{2} - 12 x + \frac{8}{x ^{2}})

Vereinfache

\frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} (21 x^{2} - 12 x + \frac{8}{x ^{2}}) : \frac{21 x ^{4} - 12 x ^{3} + 8}{2 x ^{\frac{3}{2}} 7 x ^{4} - 6 x ^{3} - 8}

= \frac{21 x ^{4} - 12 x ^{3} + 8}{2 x ^{\frac{3}{2}} 7 x ^{4} - 6 x ^{3} - 8}

4 y^{^{''}} - y^{^{'}} + y = 0

y^{^{''}} + 2 y^{^{'}} - y = 10

\frac{d y}{d x} = 1 - 9 y^{2}, y (- 1) = 0

x \to 0 lim (\frac{∣ sin ( x ) ∣}{x})

\frac{d}{d x} (- \frac{600}{x ^{2}} + 4)