derivative of 4x^3+1/(x^2-x+3)

Lösung

\frac{d}{d x} (4 x^{3} + \frac{1}{x ^{2}} - x + 3)

12 x^{2} - \frac{2}{x ^{3}} - 1

Schritte zur Lösung

\frac{d}{d x} (4 x^{3} + \frac{1}{x ^{2}} - x + 3)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (\frac{1}{x ^{2}}) - \frac{d x}{d x} + \frac{d}{d x} (3)

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (3) = 0

= 12 x^{2} - \frac{2}{x ^{3}} - 1 + 0

Vereinfache

= 12 x^{2} - \frac{2}{x ^{3}} - 1

\frac{d}{d x} (\frac{5 x}{( x ^{3} - 6 ) ^{2}})

\frac{\partial}{\partial x} (\frac{3}{2 x ^{2}})

y^{2} y^{^{'}} = x^{2}

\int_{0}^{\frac{π}{3}} x sin (12 x) d x

\int x^{\frac{2}{3}} d x