(\partial)/(\partial x)(e^{(xy)/(z^2)})

Lösung

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

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

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

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

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

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

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

y^{^{''}} = \frac{2 k}{1 - k}

\frac{d}{d x} (x^{2} ln ∣ x ∣)

d er i v a t i v e f (x) = \frac{x ^{2} + 2 x}{( x + 1 ) ^{2}}

\frac{\partial}{\partial x} (4 e^{yz} cos (x yz))

x \to 7 lim (\frac{- 2}{7 - x})