(\partial)/(\partial x)(xe^{5xy})

Lösung

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

e^{5 x y} + 5 e^{5 x y} x y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{5 x y}

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

\frac{\partial}{\partial x} (x) = 1

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

= 1 \cdot e^{5 x y} + e^{5 x y} \cdot 5 y x

Vereinfache

= e^{5 x y} + 5 e^{5 x y} x y

\int x^{2} (x^{3} + 9)^{\frac{1}{2}} d x

\int \frac{x}{( x ^{2} + 1 ) ^{3}} d x

d er i v a t i v e \frac{4.5 x - 4}{( 3 x - 4 ) ^{\frac{1}{2}}}

d er i v a t i v e e^{x} + e^{x} x

\frac{d}{d x} (\frac{9}{x ^{3}} + \frac{1}{x})