(\partial)/(\partial y)(xy+2x-ln(x^2y))

Lösung

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

x - \frac{1}{y}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (x y) = x

\frac{\partial}{\partial y} (2 x) = 0

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

= x + 0 - \frac{1}{y}

Vereinfache

= x - \frac{1}{y}

\int_{0}^{1} (sin (π x))^{2} d x

\int e^{- 4 x} x d x

\int \frac{2 x + 3}{2 x + 1} d x

\frac{\partial}{\partial y} (e^{x + y})

n = 1 \sum \infty \frac{7}{n ^{2} + 4}