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Beliebt Rechnen >

(\partial)/(\partial x)(1+xln(xy-7))

Lösung

\frac{\partial}{\partial x} (1 + x ln (x y - 7))

Lösung

\frac{x y}{x y - 7} + ln (x y - 7)

Schritte zur Lösung

\frac{\partial}{\partial x} (1 + x ln (x y - 7))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (1) + \frac{\partial}{\partial x} (x ln (x y - 7))

\frac{\partial}{\partial x} (1) = 0

\frac{\partial}{\partial x} (x ln (x y - 7)) = ln (y x - 7) + \frac{y x}{y x - 7}

= 0 + ln (y x - 7) + \frac{y x}{y x - 7}

Vereinfache

= \frac{x y}{x y - 7} + ln (x y - 7)

Beliebte Beispiele

(\partial ^2)/(\partial x\partial y)((1+2xy^2)^3)

\frac{\partial ^{2}}{\partial x \partial y} ((1 + 2 x y^{2})^{3})

sum from n=1 to infinity of 4(2.1)^{n-1}

n = 1 \sum \infty 4 (2.1)^{n - 1}

derivative of 3x^24^{-x}

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

t(dy)/(dt)=t^3+8t^3y

t \frac{d y}{d t} = t^{3} + 8 t^{3} y

integral of 9cos(θ)

\int 9 cos (θ) d θ