(\partial)/(\partial x)(sqrt(x^2+y^2-1))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

Vereinfache

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

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