(\partial)/(\partial x)(1000-4xy+xy^2)

Lösung

\frac{\partial}{\partial x} (1000 - 4 x y + x y^{2})

y^{2} - 4 y

Schritte zur Lösung

\frac{\partial}{\partial x} (1000 - 4 x y + x y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (1000) - \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (x y^{2})

\frac{\partial}{\partial x} (1000) = 0

\frac{\partial}{\partial x} (4 x y) = 4 y

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

= 0 - 4 y + y^{2}

Vereinfache

= y^{2} - 4 y

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

t an g e n t y = \frac{5}{4 x + 1}

\frac{d}{d x} (\frac{3 - 17 x ^{2}}{3 x ^{3}})

d er i v a t i v e 5 e^{x} tan (x)

\int \frac{4 x ^{2} + 3 x - 1}{x ^{3} - x ^{2}} d x