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Beliebt Rechnen >

(\partial)/(\partial x)(sqrt(x^2+y^2+2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

derivative 1/(sqrt(b-mt))

d er i v a t i v e \frac{1}{b - m t}

sum from n=5 to infinity of cos(1/(n^3))

n = 5 \sum \infty cos (\frac{1}{n ^{3}})

partialfraction (x^2)/(x^2-1)

p a r t ia l f r a c t i o n \frac{x ^{2}}{x ^{2} - 1}

derivative f(x)=(375)/(x^4)

d er i v a t i v e f (x) = \frac{375}{x ^{4}}

derivative of 10sqrt(x+5)

\frac{d}{d x} (10 x + 5)