(\partial)/(\partial x)(x^2y^3-4y)

Lösung

\frac{\partial}{\partial x} (x^{2} y^{3} - 4 y)

2 x y^{3}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} y^{3} - 4 y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{2} y^{3}) - \frac{\partial}{\partial x} (4 y)

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

\frac{\partial}{\partial x} (4 y) = 0

= 2 y^{3} x - 0

Vereinfache

= 2 x y^{3}

im pl i c i t \frac{d y}{d x}, 4 x y = 8

\int \frac{2}{x ^{3} - 5 x ^{2} + 3 x + 9} d x

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

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

\int + \frac{4 - 32 x}{1 - 16 x ^{2}} d x