(\partial)/(\partial x)(ln(x+3y+7z))

Lösung

\frac{\partial}{\partial x} (ln (x + 3 y + 7 z))

\frac{1}{x + 3 y + 7 z}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (x + 3 y + 7 z))

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

\frac{1}{x + 3 y + 7 z} \frac{\partial}{\partial x} (x + 3 y + 7 z)

= \frac{1}{x + 3 y + 7 z} \frac{\partial}{\partial x} (x + 3 y + 7 z)

\frac{\partial}{\partial x} (x + 3 y + 7 z) = 1

= \frac{1}{x + 3 y + 7 z} \cdot 1

Vereinfache

= \frac{1}{x + 3 y + 7 z}

\int tan^{3} (x) (sec (x))^{\frac{3}{2}} d x

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

x \to 0 lim (\frac{3}{0})

n = 0 \sum \infty (\frac{1}{3})^{2 n}

d er i v a t i v e \frac{5 x}{4 x ^{2} + 1}