(\partial)/(\partial y)(sqrt(8-2x^2+y^2))

Lösung

\frac{\partial}{\partial y} (8 - 2 x^{2} + y^{2})

\frac{y}{8 - 2 x ^{2} + y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (8 - 2 x^{2} + y^{2})

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{2 8 - 2 x ^{2} + y ^{2}} \frac{\partial}{\partial y} (8 - 2 x^{2} + y^{2})

= \frac{1}{2 8 - 2 x ^{2} + y ^{2}} \frac{\partial}{\partial y} (8 - 2 x^{2} + y^{2})

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

= \frac{1}{2 8 - 2 x ^{2} + y ^{2}} \cdot 2 y

Vereinfache

\frac{1}{2 8 - 2 x ^{2} + y ^{2}} \cdot 2 y : \frac{y}{8 - 2 x ^{2} + y ^{2}}

= \frac{y}{8 - 2 x ^{2} + y ^{2}}

d er i v a t i v e f (x) = x^{2} (x^{2} + 1)

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

\int_{0}^{4} x 16 - x^{2} d x

\int \frac{1 - t}{t} d t

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = - 3