(\partial)/(\partial x)(x^3y+7x^2y^2)

Lösung

\frac{\partial}{\partial x} (x^{3} y + 7 x^{2} y^{2})

3 y x^{2} + 14 y^{2} x

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} y + 7 x^{2} y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{3} y) + \frac{\partial}{\partial x} (7 x^{2} y^{2})

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

\frac{\partial}{\partial x} (7 x^{2} y^{2}) = 14 y^{2} x

= 3 y x^{2} + 14 y^{2} x

f (x) = \frac{x}{( x ^{2} - 1 ) ^{4}}

in v erse l a pl a ce \frac{( 1 )}{s ^{2}}

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

\int_{- 1}^{2} (2 + x - x^{2}) d x

x \to \frac{1}{3} lim (\frac{x + 1}{x + 2})