derivative of (3x^2-4x+5/(6sqrt(x)))

Lösung

\frac{d}{d x} (\frac{3 x ^{2} - 4 x + 5}{6 x})

\frac{9 x ^{2} - 4 x - 5}{12 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{2} - 4 x + 5}{6 x})

Entferne die Konstante:

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

= \frac{1}{6} \frac{d}{d x} (\frac{3 x ^{2} - 4 x + 5}{x})

Wende die Quotientenregel an:

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

= \frac{1}{6} \cdot \frac{\frac{d}{d x} ( 3 x ^{2} - 4 x + 5 ) x - \frac{d}{d x} ( x ) ( 3 x ^{2} - 4 x + 5 )}{( x ) ^{2}}

\frac{d}{d x} (3 x^{2} - 4 x + 5) = 6 x - 4

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

= \frac{1}{6} \cdot \frac{( 6 x - 4 ) x - \frac{1}{2 x} ( 3 x ^{2} - 4 x + 5 )}{( x ) ^{2}}

Vereinfache

\frac{1}{6} \cdot \frac{( 6 x - 4 ) x - \frac{1}{2 x} ( 3 x ^{2} - 4 x + 5 )}{( x ) ^{2}} : \frac{9 x ^{2} - 4 x - 5}{12 x x}

= \frac{9 x ^{2} - 4 x - 5}{12 x x}

x \frac{d y}{d x} + y = 9 x y^{2}

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

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 81})

y^{^{'}} - 2 y = 3 x^{2}

x \to 4 lim (x^{2} - 16)