(\partial)/(\partial y)(x^3y^5+2x^4y)

Lösung

\frac{\partial}{\partial y} (x^{3} y^{5} + 2 x^{4} y)

5 x^{3} y^{4} + 2 x^{4}

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{3} y^{5} + 2 x^{4} y)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x^{3} y^{5}) + \frac{\partial}{\partial y} (2 x^{4} y)

\frac{\partial}{\partial y} (x^{3} y^{5}) = 5 x^{3} y^{4}

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

= 5 x^{3} y^{4} + 2 x^{4}

\frac{\partial}{\partial x} (- 2 cos (x))

x \to 0 lim (sin (5 x))

\frac{d}{d x} (\frac{( x + 1 ) ( x - 2 )}{( x - 1 ) ( x + 2 )})

f (x) = e^{x - 1} - 1

y^{^{'}} - 3 y = \frac{y}{x}