derivative of (x^2-3x+1/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{x ^{2} - 3 x + 1}{x})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 3 x + 1}{x})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( 2 x - 3 ) x - \frac{1}{2 x} ( x ^{2} - 3 x + 1 )}{( x ) ^{2}} : \frac{3 x ^{2} - 3 x - 1}{2 x x}

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

x \to 5 lim (\frac{1}{( x - 5 ) ^{2}})

\int \frac{x ^{2}}{2 1 - x ^{2}} d x

\frac{d}{d x} (\frac{x}{2 π})

\int \frac{b}{b ^{2} - 2 b + 2}

\int 3 x^{2} (x^{3} + 8)^{5} d x