derivative of (5x+1/(2sqrt(x)))

Lösung

\frac{d}{d x} (\frac{5 x + 1}{2 x})

\frac{5 x - 1}{4 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 x + 1}{2 x})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (5 x + 1) = 5

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

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

Vereinfache

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

= \frac{5 x - 1}{4 x x}

l a pl a ce t r an s f or m e^{3 - t}

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

\frac{\partial ^{2}}{\partial x ^{2}} (sin^{2} (m x + n y))

in v erse l a pl a ce \frac{1}{( s - 1 ) ^{5}}

\frac{d}{d x} (2 x^{3} - 5 x)