(\partial)/(\partial x)(x^2+y^2-ycos(x))

Lösung

\frac{\partial}{\partial x} (x^{2} + y^{2} - y cos (x))

2 x + y sin (x)

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} + y^{2} - y cos (x))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (y^{2}) - \frac{\partial}{\partial x} (y cos (x))

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (y^{2}) = 0

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

= 2 x + 0 - (- y sin (x))

Vereinfache

= 2 x + y sin (x)

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

x y^{^{'}} = ((1 - x) y + x^{2} + x^{3}), y (3) = 2

x \to 3 - lim (\frac{x}{∣ x ∣})

\frac{\partial}{\partial x} (2 y^{7} + 7 y^{9} x^{6})

\int 2 x (x + 1) d x