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Beliebt Rechnen >

derivative f(x)=5x^5+2/(sqrt(x))

Lösung

ableitung von

f (x) = 5 x^{5} + \frac{2}{x}

Lösung

\frac{- 1 + 25 x ^{\frac{11}{2}}}{x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (5 x^{5} + \frac{2}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (5 x^{5}) + \frac{d}{d x} (\frac{2}{x})

\frac{d}{d x} (5 x^{5}) = 25 x^{4}

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

= 25 x^{4} - \frac{1}{x ^{\frac{3}{2}}}

Vereinfache

25 x^{4} - \frac{1}{x ^{\frac{3}{2}}} : \frac{- 1 + 25 x ^{\frac{11}{2}}}{x ^{\frac{3}{2}}}

= \frac{- 1 + 25 x ^{\frac{11}{2}}}{x ^{\frac{3}{2}}}

Graph

Beliebte Beispiele

(\partial)/(\partial x)((x^2+y^2)^5)

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{5})

derivative y=sqrt(x^2-x+9)

d er i v a t i v e y = x^{2} - x + 9

(dy)/((5-3y)^2)=(dx)/(2(4-x))

\frac{d y}{( 5 - 3 y ) ^{2}} = \frac{d x}{2 ( 4 - x )}

laplacetransform e^{-0.75t}cos(4t)

l a pl a ce t r an s f or m e^{- 0.75 t} cos (4 t)

tangent f(x)= 1/2 x^2,\at x=2

t an g e n t f (x) = \frac{1}{2} x^{2}, at x = 2