(\partial)/(\partial x)(ae^{ax+y})

Lösung

\frac{\partial}{\partial x} (a e^{a x + y})

a^{2} e^{a x + y}

Schritte zur Lösung

\frac{\partial}{\partial x} (a e^{a x + y})

Behandle

a, y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

e^{a x + y} \frac{\partial}{\partial x} (a x + y)

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

\frac{\partial}{\partial x} (a x + y) = a

= a e^{a x + y} a

Vereinfache

a e^{a x + y} a : a^{2} e^{a x + y}

= a^{2} e^{a x + y}

\frac{d}{d y} (\frac{cy ( x )}{x ^{2} + y ^{2}})

\int \frac{1}{tan ^{2} ( x ) + 1} d x

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (1) = 0, y^{^{'}} (1) = 1

\int e^{- x} cos (- x) d x

\frac{d y}{d x} = e^{8 x - 8 y}