(\partial)/(\partial x)((z)(x+sin(x+z)))

Lösung

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

z (1 + cos (x + z))

Schritte zur Lösung

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

Behandle

z

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= z (1 + cos (x + z))

e x p an d \frac{1}{( ( s - 1 ) ( s ^{2} + 1 ) )}

e x p an d \frac{1}{5 x} (5)

e x p an d \frac{( ( s - 1 ) e ^{- 2 s} )}{s ^{2} + 8 s + 13}

e x p an d \frac{( 2 x - 1 )}{x ^{2} ( x ^{2} + 1 )}

e x p an d \frac{3.2 k}{( s ^{2} + 8 s + 1 ) ( s ^{2} + s + 3 ) + 3.2 k}