(\partial)/(\partial x)(e^{sqrt(5xy)})

Lösung

\frac{\partial}{\partial x} (e^{5 x y})

\frac{5 e ^{5 x y} y}{2 x}

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{5 x y})

Vereinfache

e^{5 x y} : e^{5 x y}

= \frac{\partial}{\partial x} (e^{5 x y})

Behandle

y

als Konstante

Wende die Kettenregel an:

e^{5 x y} \frac{\partial}{\partial x} (5 x y)

= e^{5 x y} \frac{\partial}{\partial x} (5 x y)

\frac{\partial}{\partial x} (5 x y) = 5 \frac{1}{2 x y} y

= e^{5 x y} 5 \frac{1}{2 x y} y

Vereinfache

e^{5 x y} 5 \frac{1}{2 x y} y : \frac{5 e ^{5 x y} y}{2 x}

= \frac{5 e ^{5 x y} y}{2 x}

\int \frac{1}{1 + 4 t ^{2}} d t

(x + y) d x + x^{2} d y = 0

\frac{\partial}{\partial x} (1 (x - y) \cdot e^{1 y + 4 x^{2}})

\frac{d ^{3}}{d x ^{3}} (6 x + 3)

\int_{0}^{s i n (x)} 8 t d t