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

Lösung

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

ln (2) \cdot 2^{y}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (2^{x}) = 0

\frac{\partial}{\partial y} (2^{y}) = 2^{y} ln (2)

= 0 + 2^{y} ln (2)

Vereinfache

= ln (2) \cdot 2^{y}

x \to 2 lim (\frac{x - 3}{x ^{2} - 9})

\frac{d}{d x} (\frac{e ^{x}}{e ^{x} + e ^{y} + e ^{z}})

\frac{d y}{d x} = 3 x^{7} y - y, y (1) = - 9

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 e^{- 2 x}

\int \frac{6 x ^{3} + 4 x ^{2} - 45 x - 33}{x ^{2} - 9} d x