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Beliebt Rechnen >

derivative of x/(sqrt(x-7))

Lösung

\frac{d}{d x} (\frac{x}{x - 7})

Lösung

\frac{x - 14}{2 ( x - 7 ) x - 7}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x - 7})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} x - 7 - \frac{d}{d x} ( x - 7 ) x}{( x - 7 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x - 7) = \frac{1}{2 x - 7}

= \frac{1 \cdot x - 7 - \frac{1}{2 x - 7} x}{( x - 7 ) ^{2}}

Vereinfache

\frac{1 \cdot x - 7 - \frac{1}{2 x - 7} x}{( x - 7 ) ^{2}} : \frac{x - 14}{2 ( x - 7 ) x - 7}

= \frac{x - 14}{2 ( x - 7 ) x - 7}

Graph

Beliebte Beispiele

integral of (2x-1)/(4x^2-1)

\int \frac{2 x - 1}{4 x ^{2} - 1} d x

(\partial)/(\partial y)(5xy^2)

\frac{\partial}{\partial y} (5 x y^{2})

integral of (35)/(1-cos(5x))

\int \frac{35}{1 - cos ( 5 x )} d x

derivative of x^5+x+1

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

derivative of (((0.06x^2+17x+340))/x)

\frac{d}{d x} (\frac{( ( 0.06 x ^{2} ) + 17 x + 340 )}{x})