(\partial)/(\partial y)(e^{xy}-(x+1)cos(y))

Lösung

\frac{\partial}{\partial y} (e^{x y} - (x + 1) cos (y))

e^{x y} x + sin (y) (x + 1)

Schritte zur Lösung

\frac{\partial}{\partial y} (e^{x y} - (x + 1) cos (y))

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (e^{x y}) - \frac{\partial}{\partial y} ((x + 1) cos (y))

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

\frac{\partial}{\partial y} ((x + 1) cos (y)) = - sin (y) (x + 1)

= e^{x y} x - (- sin (y) (x + 1))

Vereinfache

= e^{x y} x + sin (y) (x + 1)

x \to 0 lim (\frac{x ^{3} + 7 x}{x})

a re a y = x^{2} - 5, y = 4

\int_{6}^{8} \frac{64}{( x - 6 ) ^{3}} d x

\int x cos (3 x + 1) d x

\frac{d}{d x} (5 ln (6 - x^{2}))