(\partial)/(\partial y)((A^2x^2+B^2y^2)^4)

Lösung

\frac{\partial}{\partial y} ((A^{2} x^{2} + B^{2} y^{2})^{4})

8 B^{2} y (A^{2} x^{2} + B^{2} y^{2})^{3}

Schritte zur Lösung

\frac{\partial}{\partial y} ((A^{2} x^{2} + B^{2} y^{2})^{4})

Behandle

A, B, x

als Konstante

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (A^{2} x^{2} + B^{2} y^{2}) = 2 B^{2} y

= 4 (A^{2} x^{2} + B^{2} y^{2})^{3} \cdot 2 B^{2} y

Vereinfache

= 8 B^{2} y (A^{2} x^{2} + B^{2} y^{2})^{3}

\int \frac{e ^{\frac{4}{x}}}{x ^{2}} d x

\int \frac{1}{x ^{2}} - 3 x d x

x \to - \infty lim (xx)

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

in v erse l a pl a ce \frac{s + 7}{( s + 2 ) ( s - 5 )}