(\partial)/(\partial x)(e^{xcos(y)}sin(xy))

Lösung

\frac{\partial}{\partial x} (e^{x c o s (y)} sin (x y))

e^{x c o s (y)} cos (y) sin (x y) + cos (x y) y e^{x c o s (y)}

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{x c o s (y)} sin (x y))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = e^{x c o s (y)}, g = sin (x y)

= \frac{\partial}{\partial x} (e^{x c o s (y)}) sin (x y) + \frac{\partial}{\partial x} (sin (x y)) e^{x c o s (y)}

\frac{\partial}{\partial x} (e^{x c o s (y)}) = e^{x c o s (y)} cos (y)

\frac{\partial}{\partial x} (sin (x y)) = cos (x y) y

= e^{x c o s (y)} cos (y) sin (x y) + cos (x y) y e^{x c o s (y)}

d er i v a t i v e (x^{2} - 4)^{2}

\int \frac{9 x ^{3} - x ^{2} + 45 x + 5}{x ^{3} + 5 x} d x

x \to 2 lim (x^{4} - 16)

\int 5 t e^{t} d t

x \to 6 - lim (\frac{x + 1}{x - 6})