(\partial)/(\partial x)(ln(6x^2-4y^2))

Lösung

\frac{\partial}{\partial x} (ln (6 x^{2} - 4 y^{2}))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (6 x^{2} - 4 y^{2}))

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{6 x ^{2} - 4 y ^{2}} \frac{\partial}{\partial x} (6 x^{2} - 4 y^{2})

= \frac{1}{6 x ^{2} - 4 y ^{2}} \frac{\partial}{\partial x} (6 x^{2} - 4 y^{2})

\frac{\partial}{\partial x} (6 x^{2} - 4 y^{2}) = 12 x

= \frac{1}{6 x ^{2} - 4 y ^{2}} \cdot 12 x

Vereinfache

\frac{1}{6 x ^{2} - 4 y ^{2}} \cdot 12 x : \frac{6 x}{3 x ^{2} - 2 y ^{2}}

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

x \to 7 lim (\frac{9 x}{x - 7})

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

d er i v a t i v e y = x^{\frac{17}{18}}

\frac{\partial}{\partial y} (y \cdot ln (x))

\frac{d}{d x} (\frac{1}{3} (16 + x^{2})^{3})