(\partial)/(\partial x)(x^{-1}y^2+xy^2+3xy)

Lösung

\frac{\partial}{\partial x} (x^{- 1} y^{2} + x y^{2} + 3 x y)

- \frac{y ^{2}}{x ^{2}} + y^{2} + 3 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{- 1} y^{2} + x y^{2} + 3 x y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{- 1} y^{2}) + \frac{\partial}{\partial x} (x y^{2}) + \frac{\partial}{\partial x} (3 x y)

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

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

\frac{\partial}{\partial x} (3 x y) = 3 y

= - \frac{y ^{2}}{x ^{2}} + y^{2} + 3 y

\int \frac{x ^{2} - x + 5}{x} d x

n = 1 \sum \infty \frac{n}{n + 5}

\frac{d}{d x} (- \frac{4}{3} sin (x) - \frac{5}{3} cos (x))

x \to + 3 lim (x^{2} + 4)

\frac{\partial}{\partial x} (\frac{a x + b y}{( c x + d y )})