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

Lösung

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

\frac{3 x}{3 x ^{2} + 2 y ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 3 x ^{2} + 2 y ^{2}} \frac{\partial}{\partial x} (3 x^{2} + 2 y^{2})

= \frac{1}{2 3 x ^{2} + 2 y ^{2}} \frac{\partial}{\partial x} (3 x^{2} + 2 y^{2})

\frac{\partial}{\partial x} (3 x^{2} + 2 y^{2}) = 6 x

= \frac{1}{2 3 x ^{2} + 2 y ^{2}} \cdot 6 x

Vereinfache

\frac{1}{2 3 x ^{2} + 2 y ^{2}} \cdot 6 x : \frac{3 x}{3 x ^{2} + 2 y ^{2}}

= \frac{3 x}{3 x ^{2} + 2 y ^{2}}

a re a y = x^{2} - 3 x, y = 4 x

(x^{2} + 1) \frac{d y}{d x} + 7 x (y - 1) = 0, y (0) = 9

\int x^{2} e^{21 x} d x

2 y^{^{'}} + t y = 2

\int_{4}^{9} \frac{1}{x} d x