(\partial)/(\partial x)(y/x+e^{xy}+xy^2)

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

\frac{d}{d x} (\frac{1}{3} tan^{3} (x))

n = 1 \sum \infty n!^{2} (5^{n})

d er i v a t i v e x^{2} e^{- x} + (ln (x))^{2}

\int 3 s h^{3} x d x

y^{^{'}} = 5 x