(\partial)/(\partial x)(xcos(x)sin(x))

Lösung

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

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

Schritte zur Lösung

\frac{\partial}{\partial 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{\partial}{\partial x} (x) cos (x) sin (x) + \frac{\partial}{\partial x} (cos (x) sin (x)) x

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

\frac{\partial}{\partial 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)

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

d er i v a t i v e x^{2} - 5

\frac{d}{d x} ((2 x)^{3 x})

\frac{d}{d x} (5 x - 9)

y^{^{''}} - 5 y^{^{'}} + 6 y = sin (x)