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Beliebt Rechnen >

(\partial)/(\partial x)(xy+ln(x+y))

Lösung

\frac{\partial}{\partial x} (x y + ln (x + y))

Lösung

y + \frac{1}{x + y}

Schritte zur Lösung

\frac{\partial}{\partial x} (x y + ln (x + y))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= y + \frac{1}{x + y}

Beliebte Beispiele

derivative of sin^{ln(x}(3x))

\frac{d}{d x} (sin^{l n (x)} (3 x))

integral of sin(sqrt(at))

\int sin (a t) d t

derivative of e^{3x}+10e^{2x}

\frac{d}{d x} (e^{3 x} + 10 e^{2 x})

t^2y^'+3ty+2t^3=0

t^{2} y^{^{'}} + 3 t y + 2 t^{3} = 0

(e^y+6x)dx+(xe^y)dy=0

(e^{y} + 6 x) d x + (x e^{y}) d y = 0