d/(d{x)}(({z})(-e^{{z}}+{x}^2+{y}^2+{z}^2))

Lösung

\frac{d}{d x} ((z) (- e^{z} + x^{2} + y^{2} + z^{2}))

2 z x

Schritte zur Lösung

\frac{d}{d x} ((z) (- e^{z} + x^{2} + y^{2} + z^{2}))

Entferne die Konstante:

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

= z \frac{d}{d x} (- e^{z} + x^{2} + y^{2} + z^{2})

Wende die Summen-/Differenzregel an:

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

= z (- \frac{d}{d x} (e^{z}) + \frac{d}{d x} (x^{2}) + \frac{d}{d x} (y^{2}) + \frac{d}{d x} (z^{2}))

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (y^{2}) = 0

\frac{d}{d x} (z^{2}) = 0

= z (- 0 + 2 x + 0 + 0)

Vereinfache

= 2 z x

e x p an d - \frac{16 x}{( x ^{2} + 4 ) ( - x ^{2} + 4 )}

e x p an d \frac{5 ( 10 a + 11 b )}{9}

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

\frac{d}{d x} ((z (x, y)) (2 x^{2} y^{3} + x^{2} y))

e x p an d (f (x) + g (x)) (f (x) (x) x)^{'}