(\partial)/(\partial x)(sqrt((x+4)/(x+5)))

Lösung

\frac{\partial}{\partial x} (\frac{x + 4}{x + 5})

\frac{1}{2 x + 4 ( x + 5 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x + 4}{x + 5})

Wende die Kettenregel an:

\frac{1}{2 \frac{x + 4}{x + 5}} \frac{\partial}{\partial x} (\frac{x + 4}{x + 5})

= \frac{1}{2 \frac{x + 4}{x + 5}} \frac{\partial}{\partial x} (\frac{x + 4}{x + 5})

\frac{\partial}{\partial x} (\frac{x + 4}{x + 5}) = \frac{1}{( x + 5 ) ^{2}}

= \frac{1}{2 \frac{x + 4}{x + 5}} \cdot \frac{1}{( x + 5 ) ^{2}}

Vereinfache

\frac{1}{2 \frac{x + 4}{x + 5}} \cdot \frac{1}{( x + 5 ) ^{2}} : \frac{1}{2 x + 4 ( x + 5 ) ^{\frac{3}{2}}}

= \frac{1}{2 x + 4 ( x + 5 ) ^{\frac{3}{2}}}

\frac{\partial}{\partial y} (sin (\frac{y}{x}))

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

t an g e n t (3 x^{2} + 2 x), at (a = - 3)

a re a y = x, y = x - 2, [0, 4]

\frac{\partial}{\partial x} (2 x^{2} + 4 y^{2} - 3 z^{2} - 11)