derivative y=(x+x^2)^{1/2}

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e lo g_{10} (sin (x^{2}))

d er i v a t i v e 5 sin (x + 1)

d er i v a t i v e \frac{l}{800}

d er i v a t i v e y = - 50

d er i v a t i v e x^{\frac{- 1}{3}}