(\partial)/(\partial y)(xsqrt(1+y^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial y} (sin (x) cos (7 y))

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