derivative y=xcos(x)sin(x)

Lösung

ableitung von

y = x cos (x) sin (x)

cos (x) sin (x) + x cos (2 x)

Schritte zur Lösung

\frac{d}{d x} (x cos (x) sin (x))

Wende die Produktregel an:

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

f = x, g = cos (x) sin (x)

= \frac{d x}{d x} cos (x) sin (x) + \frac{d}{d x} (cos (x) sin (x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (cos (x) sin (x)) = cos (2 x)

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

Vereinfache

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

\frac{\partial}{\partial y} (4 y (\frac{1}{x} - ln (x)))

\int_{0}^{9} \frac{1}{x} d x

d er i v a t i v e y = sec (x) tan (x)

\int 7 e^{3 x} d x

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