(\partial)/(\partial x)(xcos(x+2y))

Lösung

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

cos (x + 2 y) - x sin (x + 2 y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = cos (x + 2 y)

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

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

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

= 1 \cdot cos (x + 2 y) + (- sin (x + 2 y)) x

Vereinfache

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

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

d er i v a t i v e f (x) = 5 sec (x)

d er i v a t i v e g (x) = - 8 x^{2} - x + 8

x \to 2 lim (\frac{3}{x - 2})

d er i v a t i v e \frac{ln ( 4 x )}{4 x}