(\partial)/(\partial x)(cos(xy)x)

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = cos (x y), g = x

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

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

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

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

Vereinfache

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

(3 x^{2} - 12)^{^{'}}

d er i v a t i v e x^{2} 49 - x^{2}

\int_{0}^{\frac{π}{2}} 2 cos^{2} (x) d x

x \to - 0 lim (\frac{6 x}{x ^{4}})

in v erse l a pl a ce \frac{- 4 e ^{(- s)} \cdot ( e ^{3} )}{( ( s - 3 ) ( s - 4 ) ( s + 1 ) )}