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

Lösung

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

45 x^{2} y (5 x^{3} y + 4 y^{5})^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (5 x^{3} y + 4 y^{5}) = 15 y x^{2}

= 3 (5 x^{3} y + 4 y^{5})^{2} \cdot 15 y x^{2}

Vereinfache

= 45 x^{2} y (5 x^{3} y + 4 y^{5})^{2}

l a pl a ce t r an s f or m sin^{2} (6 t)

\frac{d}{d x} (e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x})

\frac{d}{d x} (x^{3} + x^{5})

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

\frac{\partial}{\partial x} (\frac{x ^{2}}{x ^{2} + 1})