(\partial)/(\partial y)(sqrt(4x^2+6xy+y^2))

Lösung

\frac{\partial}{\partial y} (4 x^{2} + 6 x y + y^{2})

\frac{y + 3 x}{4 x ^{2} + 6 x y + y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (4 x^{2} + 6 x y + y^{2})

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{2 4 x ^{2} + 6 x y + y ^{2}} \frac{\partial}{\partial y} (4 x^{2} + 6 x y + y^{2})

= \frac{1}{2 4 x ^{2} + 6 x y + y ^{2}} \frac{\partial}{\partial y} (4 x^{2} + 6 x y + y^{2})

\frac{\partial}{\partial y} (4 x^{2} + 6 x y + y^{2}) = 2 y + 6 x

= \frac{1}{2 4 x ^{2} + 6 x y + y ^{2}} (2 y + 6 x)

Vereinfache

\frac{1}{2 4 x ^{2} + 6 x y + y ^{2}} (2 y + 6 x) : \frac{y + 3 x}{4 x ^{2} + 6 x y + y ^{2}}

= \frac{y + 3 x}{4 x ^{2} + 6 x y + y ^{2}}

\frac{\partial}{\partial x} (6 x + 2 y)

\int (2 x - 2) e^{- x} d x

\frac{d}{d x} (5 x^{7} e^{x})

y^{^{'}} = 5 x + y, y (0) = 6

\int l x d x