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Beliebt Rechnen >

(\partial)/(\partial x)(log_{e}(x+y))

Lösung

\frac{\partial}{\partial x} (lo g_{e} (x + y))

Lösung

\frac{1}{x + y}

Schritte zur Lösung

\frac{\partial}{\partial x} (lo g_{e} (x + y))

Vereinfache

lo g_{e} (x + y) : ln (x + y)

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

= \frac{1}{x + y}

Beliebte Beispiele

derivative f(x)=5^{sqrt(x)}

d er i v a t i v e f (x) = 5^{x}

derivative of (4x/(x-5))

\frac{d}{d x} (\frac{4 x}{x - 5})

y^'-xy=xy^{3/2}

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

steigung 1/(sqrt(x))

s l o p e \frac{1}{x}

derivative y=9arctan(x-sqrt(1+x^2))

d er i v a t i v e y = 9 arctan (x - 1 + x^{2})