(\partial)/(\partial x)(sin(x)cos(x))

Lösung

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

cos (2 x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= cos (2 x)

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

a re a y = x, y = 3 x

\int \frac{1}{1 + tan ( β )} d β

x \to 8 lim (\frac{x ^{2} - 8 x}{x ^{3} + 2 x ^{2}})

\frac{d}{d x} (x \cdot ln (2))