(\partial)/(\partial x)((x-y)sin(3x+2y))

Lösung

\frac{\partial}{\partial x} ((x - y) sin (3 x + 2 y))

sin (3 x + 2 y) + 3 cos (3 x + 2 y) (x - y)

Schritte zur Lösung

\frac{\partial}{\partial x} ((x - y) sin (3 x + 2 y))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x - y, g = sin (3 x + 2 y)

= \frac{\partial}{\partial x} (x - y) sin (3 x + 2 y) + \frac{\partial}{\partial x} (sin (3 x + 2 y)) (x - y)

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

\frac{\partial}{\partial x} (sin (3 x + 2 y)) = cos (3 x + 2 y) \cdot 3

= 1 \cdot sin (3 x + 2 y) + cos (3 x + 2 y) \cdot 3 (x - y)

Vereinfache

= sin (3 x + 2 y) + 3 cos (3 x + 2 y) (x - y)

in v erse l a pl a ce \frac{6}{( s ^{2} ( s ^{2} + 8 s + 1 ) )}

d er i v a t i v e y = ln ∣ x ∣

t an g e n t f (x) = x - 8, at x = 12

\int x^{2} + 4 e^{x} + C d x

\frac{\partial}{\partial x} (2 \cdot x^{3} \cdot y^{2})