(\partial)/(\partial x)(sqrt(6+3x^2-2y^2))

Lösung

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

\frac{3 x}{6 + 3 x ^{2} - 2 y ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 6 + 3 x ^{2} - 2 y ^{2}} \frac{\partial}{\partial x} (6 + 3 x^{2} - 2 y^{2})

= \frac{1}{2 6 + 3 x ^{2} - 2 y ^{2}} \frac{\partial}{\partial x} (6 + 3 x^{2} - 2 y^{2})

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

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

Vereinfache

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

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

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

l a pl a ce t r an s f or m 2 t^{4}

x \frac{d y}{d x} = y + 2 x e^{- \frac{y}{x}}

\frac{d y}{d x} = x - 2.5 y

ma c l a u r in 1.5 (1 + e^{- 0.2 t})