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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d t} (2 t + 7)

\int_{1}^{2} \frac{4}{( x - 1 ) ^{\frac{1}{4}}} d x

x \to 3 + lim (\frac{3 x}{x - 3})

x \to 1 lim (\frac{x ^{m} - 1}{x - 1})

t an g e n t f (x) = \frac{x ^{2}}{x - 3}, at x = 0