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Beliebt Rechnen >

derivative f(x)=12sqrt(x^3)-1/x

Lösung

ableitung von

f (x) = 12 x^{3} - \frac{1}{x}

Lösung

18 x + \frac{1}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (12 x^{3} - \frac{1}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (12 x^{3}) - \frac{d}{d x} (\frac{1}{x})

\frac{d}{d x} (12 x^{3}) = 18 x

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

= 18 x - (- \frac{1}{x ^{2}})

Vereinfache

= 18 x + \frac{1}{x ^{2}}

Graph

Beliebte Beispiele

derivative x^2+2x+2

d er i v a t i v e x^{2} + 2 x + 2

derivative (126-0.5x)x-50x-31.75

d er i v a t i v e (126 - 0.5 x) x - 50 x - 31.75

1-(dv)/(dx)=cos(v)

1 - \frac{d v}{d x} = cos (v)

(d^2)/(dx^2)(sqrt(x^2+9))

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

tangent f(x)=-x^2-x+3,\at x=-3

t an g e n t f (x) = - x^{2} - x + 3, at x = - 3