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Beliebt Rechnen >

(\partial)/(\partial x)(ln(x^2+y^2+1))

Lösung

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

Lösung

\frac{2 x}{x ^{2} + y ^{2} + 1}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

= \frac{1}{x ^{2} + y ^{2} + 1} \cdot 2 x

Vereinfache

\frac{1}{x ^{2} + y ^{2} + 1} \cdot 2 x : \frac{2 x}{x ^{2} + y ^{2} + 1}

= \frac{2 x}{x ^{2} + y ^{2} + 1}

Beliebte Beispiele

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

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

derivative y=2x-4

d er i v a t i v e y = 2 x - 4

derivative of 1/(sqrt(x^2+5))

\frac{d}{d x} (\frac{1}{x ^{2} + 5})

limit as x approaches 1 of (x^5-1)/(x-1)

x \to 1 lim (\frac{x ^{5} - 1}{x - 1})

derivative f(x)=xsin(2^x)

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