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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (x^{2} + 6 x y + 4 y^{2}) = 8 y + 6 x

= \frac{1}{2 x ^{2} + 6 x y + 4 y ^{2}} (8 y + 6 x)

Vereinfache

\frac{1}{2 x ^{2} + 6 x y + 4 y ^{2}} (8 y + 6 x) : \frac{4 y + 3 x}{x ^{2} + 6 x y + 4 y ^{2}}

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

\int x^{2} + 2 x + 1 d x

\int_{0}^{1} \frac{2 y}{e ^{2 y}} d y

y^{^{'}} + \frac{3}{t} y = 0

x \to 3 lim (x^{5})

\int_{1}^{e} ln (x) d x