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Beliebt Rechnen >

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

Lösung

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

Lösung

8 x - \frac{2}{x ^{3}} + 12 x^{3}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 8 x - \frac{2}{x ^{3}} + 12 x^{3}

Graph

Beliebte Beispiele

derivative of 8x-5

\frac{d}{d x} (8 x - 5)

derivative of tan(x^x)

\frac{d}{d x} (tan (x^{x}))

3x(xy-2)dx+(x^3+2y)dy=0

3 x (x y - 2) d x + (x^{3} + 2 y) d y = 0

derivative of (arcsec((x^2/2))^{3x})

\frac{d}{d x} ((arcsec (\frac{x ^{2}}{2}))^{3 x})

integral of e^{sin(x)}sin(2x)

\int e^{s i n (x)} sin (2 x) d x