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Beliebt Rechnen >

(\partial)/(\partial x)(ln(x^2+y)-z)

Lösung

\frac{\partial}{\partial x} (ln (x^{2} + y) - z)

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (x^{2} + y) - z)

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (ln (x^{2} + y)) - \frac{\partial}{\partial x} (z)

\frac{\partial}{\partial x} (ln (x^{2} + y)) = \frac{2 x}{x ^{2} + y}

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

= \frac{2 x}{x ^{2} + y} - 0

Vereinfache

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

Beliebte Beispiele

limit as x approaches 3 of sqrt(x^2+9)

x \to 3 lim (x^{2} + 9)

derivative 2sin^2(x)

d er i v a t i v e 2 sin^{2} (x)

f (y) = \frac{1}{2 y}

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

\frac{d}{d x} (9 arctan (x - 1 + x^{2}))

integral of x^4+x+9

\int x^{4} + x + 9 d x