(\partial)/(\partial x)(xyz-cos(x+y+z))

Lösung

\frac{\partial}{\partial x} (x yz - cos (x + y + z))

yz + sin (x + y + z)

Schritte zur Lösung

\frac{\partial}{\partial x} (x yz - cos (x + y + z))

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= yz - (- sin (x + y + z))

Vereinfache

= yz + sin (x + y + z)

\int - g e^{- c t} \frac{1}{c} d t

\frac{\partial}{\partial x} (4 x^{2} + 2 x y - 8 y^{2})

\frac{\partial}{\partial x} (- \frac{y}{x ^{2} + y ^{2}})

\frac{\partial}{\partial x} (tan (4 + 2 x^{2} y^{4} z^{2}))

x \to 0 lim (\frac{sin ^{4} ( 2 x )}{4 x ^{4}})