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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

\frac{d}{d x} (3 x^{2} + 6 x + 6)

\frac{d y}{d x} y = \frac{4 x}{3 x - 2 x ^{2}}

\frac{d}{d x} (1.4 x^{5} - 2.5 x^{2} + 6.7)

d er i v a t i v e x^{2} + 4