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

Lösung

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

x \to + (- 1) lim (x + 2 x^{4})

t an g e n t - \frac{1}{( x - 5 ) ^{2}}

\frac{d}{d x} (e^{x^{0}})

\int_{1}^{3} \frac{x}{( 2 x - 1 ) ^{3}} d x

\int x ln (5 x) d x