(\partial)/(\partial x)(ln(1+x^2+e^y+z))

Lösung

\frac{\partial}{\partial x} (ln (1 + x^{2} + e^{y} + z))

\frac{2 x}{1 + x ^{2} + e ^{y} + z}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (1 + x^{2} + e^{y} + z))

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{2 x}{1 + x ^{2} + e ^{y} + z}

t an g e n t y = sec (x), (\frac{π}{6}, \frac{2 3}{3})

2 x y^{^{'}} - 8 y = x^{- 4}

d er i v a t i v e - \frac{1}{2 1 - x}

\int 1 + t^{4} d t

t \to 0 lim (e^{- 6 t})