derivative x(x^2-1)^{1/2}

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (x^{2} - 1)^{\frac{1}{2}}

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

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

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

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

Vereinfache

1 \cdot (x^{2} - 1)^{\frac{1}{2}} + \frac{x}{( x ^{2} - 1 ) ^{\frac{1}{2}}} x : \frac{2 x ^{2} - 1}{( x ^{2} - 1 ) ^{\frac{1}{2}}}

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

\frac{d}{d q} ((1 + csc (q)) cos (q))

d er i v a t i v e \frac{sin ( x )}{2}

d er i v a t i v e ln (x^{3} (2 x - 5)^{4})

d er i v a t i v e y = x (4 x - 3)

d er i v a t i v e \frac{- cos ( x )}{sin ^{2} ( x )}