(\partial)/(\partial x)(x^3-5x^2y+7xy^3)

Lösung

\frac{\partial}{\partial x} (x^{3} - 5 x^{2} y + 7 x y^{3})

3 x^{2} - 10 y x + 7 y^{3}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} - 5 x^{2} y + 7 x y^{3})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{3}) - \frac{\partial}{\partial x} (5 x^{2} y) + \frac{\partial}{\partial x} (7 x y^{3})

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

\frac{\partial}{\partial x} (5 x^{2} y) = 10 y x

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

= 3 x^{2} - 10 y x + 7 y^{3}

\int \frac{1}{2 - e ^{- x}} d x

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

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

\int \frac{1}{x ( ln ( x ^{6} ) ) ^{8}} d x

\int \frac{2 x ^{1}}{( x ^{5} ) ^{3}} d x