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Beliebt Rechnen >

derivative f(x)=sqrt(x)+1/(sqrt(x^3))

Lösung

ableitung von

f (x) = x + \frac{1}{x ^{3}}

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Graph

Beliebte Beispiele

fläche x=2y,x=y^2-3

a re a x = 2 y, x = y^{2} - 3

integral of 2x^2+5x

\int 2 x^{2} + 5 x d x

(dy)/(dx)=(e^x)/(e^y)

\frac{d y}{d x} = \frac{e ^{x}}{e ^{y}}

tangent y=x^4+4x^2-x,(1,4)

t an g e n t y = x^{4} + 4 x^{2} - x, (1, 4)

tangent y= 1/3 x^3-3x^2+5x

t an g e n t y = \frac{1}{3} x^{3} - 3 x^{2} + 5 x