(\partial)/(\partial x)((w)(u(w,v,x)^2+e^{2v}))

Lösung

\frac{\partial}{\partial x} ((w) (u (w, v, x) (w, v, x)^{2} + e^{2 v}))

w ((\frac{\partial}{\partial x} (u (w, v, x)) (w, v, x)^{2} + 2 (w, v, x) (w, v, 1) u (w, v, x)) + 0)

Schritte zur Lösung

\frac{\partial}{\partial x} ((w) (u (w, v, x) (w, v, x)^{2} + e^{2 v}))

Behandle

w, v

als Konstanten

Entferne die Konstante:

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

= w \frac{\partial}{\partial x} (u (w, v, x) (w, v, x)^{2} + e^{2 v})

Wende die Summen-/Differenzregel an:

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

= w (\frac{\partial}{\partial x} (u (w, v, x) (w, v, x)^{2}) + \frac{\partial}{\partial x} (e^{2 v}))

\frac{\partial}{\partial x} (u (w, v, x) (w, v, x)^{2}) = \frac{\partial}{\partial x} (u (w, v, x)) (w, v, x)^{2} + 2 (w, v, x) (w, v, 1) u (w, v, x)

\frac{\partial}{\partial x} (e^{2 v}) = 0

= w ((\frac{\partial}{\partial x} (u (w, v, x)) (w, v, x)^{2} + 2 (w, v, x) (w, v, 1) u (w, v, x)) + 0)

e x p an d 2 sec^{2} (x) tan^{2} (x) (tan (x) + sec (x))

e x p an d \frac{x ^{n + 1}}{( n + 1 ) n !}

e x p an d \frac{( 18 n - 7 ) ^{2}}{441}

e x p an d \frac{e ^{- 5 s} ( 2 s + 3 )}{s ( s ^{2} + 2 s + 5 )}

\frac{d}{d y} ((x (y)) (\frac{y ^{4}}{4} + \frac{1}{8 y ^{2}}))