(\partial)/(\partial x)(8xcos(x)cos(y))

Lösung

\frac{\partial}{\partial x} (8 x cos (x) cos (y))

8 cos (y) (cos (x) - x sin (x))

Schritte zur Lösung

\frac{\partial}{\partial x} (8 x cos (x) cos (y))

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 cos (y) \frac{\partial}{\partial x} (x cos (x))

Wende die Produktregel an:

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

f = x, g = cos (x)

= 8 cos (y) (\frac{\partial}{\partial x} (x) cos (x) + \frac{\partial}{\partial x} (cos (x)) x)

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

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

= 8 cos (y) (1 \cdot cos (x) + (- sin (x)) x)

Vereinfache

= 8 cos (y) (cos (x) - x sin (x))

x \to 1 lim (\frac{∣ x ∣}{x})

x \to 0 lim (h (\frac{1}{x}))

\int 5 x^{3} e^{x^{4}} d x

\frac{d}{d t} (\frac{5}{5 - t})

\int 4 - 25 x^{2} d x