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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\frac{d}{d x} (- \frac{10 x}{( x ^{2} - 9 ) ^{2}})

\frac{d}{d x} (3 x^{3} - 9 x)

t a y l or sin (cos (x))

x \to 0 - lim (e^{\frac{9}{x}})

x \to \infty lim (x \cdot 0)