derivative of 1/(x+sqrt(x))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e \frac{125}{x ^{2} + 49}

\int x^{2} 4 x + 6 d x

\int 3 z^{2} sin (x) - 4 d z

d er i v a t i v e f (x) = 4 x^{5 x}

y^{^{'}} + y cos (x) = 2 cos (x), y (0) = 4