implicit (dy)/(dx),ysin(1/y)=1-xy

Lösung

implizite ableitung

\frac{d y}{d x}, y sin (\frac{1}{y}) = 1 - x y

\frac{d y}{d x} = - \frac{y ^{2}}{y sin ( \frac{1}{y} ) - cos ( \frac{1}{y} ) + x y}

Schritte zur Lösung

y sin (\frac{1}{y}) = 1 - x y

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

sin (\frac{1}{y}) \frac{d y}{d x} - \frac{cos ( \frac{1}{y} ) \frac{d y}{d x}}{y} = - x \frac{d y}{d x} - y

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y ^{2}}{y sin ( \frac{1}{y} ) - cos ( \frac{1}{y} ) + x y}

\frac{d y}{d x} = - \frac{y ^{2}}{y sin ( \frac{1}{y} ) - cos ( \frac{1}{y} ) + x y}

\frac{d}{d x} (lo g_{8} (x))

\int 7 e^{- 0.5 x} d x

7 y^{^{''}} + 13 y^{^{'}} - 2 y = 0

s im pl i f y 2 t^{- \frac{1}{4}}

\int_{0}^{π} cos^{4} (2 x) d x