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Beliebt Rechnen >

(\partial)/(\partial x)((2x-3)/(xy))

Lösung

\frac{\partial}{\partial x} (\frac{2 x - 3}{x y})

Lösung

\frac{3}{x ^{2} y}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{2 x - 3}{x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= \frac{1}{y} \frac{\partial}{\partial x} (\frac{2 x - 3}{x})

Wende die Quotientenregel an:

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

= \frac{1}{y} \cdot \frac{\frac{\partial}{\partial x} ( 2 x - 3 ) x - \frac{\partial}{\partial x} ( x ) ( 2 x - 3 )}{x ^{2}}

\frac{\partial}{\partial x} (2 x - 3) = 2

\frac{\partial}{\partial x} (x) = 1

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

Vereinfache

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

= \frac{3}{x ^{2} y}

Beliebte Beispiele

derivative sqrt(7-3u)

d er i v a t i v e 7 - 3 u

(\partial)/(\partial y)(x^2y+3y+x^2y^3-4x)

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

y^{''}+y^'-2y=2t,y(0)=0,y^'(0)=7

y^{^{''}} + y^{^{'}} - 2 y = 2 t, y (0) = 0, y^{^{'}} (0) = 7

tangent y=x^3-2x+2(2.6)

t an g e n t y = x^{3} - 2 x + 2 (2.6)

derivative of x+2/(sin(x))

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