derivative of sqrt(x)+4/(sqrt(x)+4)

Lösung

\frac{d}{d x} (x + \frac{4}{x} + 4)

\frac{1}{2 x} - \frac{2}{x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (x + \frac{4}{x} + 4)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x) + \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (4)

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

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

\frac{d}{d x} (4) = 0

= \frac{1}{2 x} - \frac{2}{x ^{\frac{3}{2}}} + 0

Vereinfache

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

\int \frac{25 + x ^{2}}{x} d x

\frac{\partial}{\partial y} (x 1 + y^{7})

t an g e n t f (x) = \frac{6 x}{x + 2}, at x = 4

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x}

(5 y - 2 x) d y - 2 y d x = 0