d/(d{x)}(({z})(ln({x}^2+{z}^2)+{y}{z}^3+2{x}^2))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (y z^{3}) = 0

\frac{d}{d x} (2 x^{2}) = 4 x

= z (\frac{2 x}{x ^{2} + z ^{2}} + 0 + 4 x)

Vereinfache

= z (\frac{2 x}{x ^{2} + z ^{2}} + 4 x)

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

e x p an d \frac{sin ^{2} ( θ ) + ( 1 + cos ( θ ) ) ^{2}}{cos ( θ ) + 1}

e x p an d \frac{2 x ^{2} + 6 x}{( x - 3 ) ( x + 1 )}

e x p an d (1 - x^{2})^{\frac{1}{2}} (1 + x^{3})

s im pl i f y - 2 (3 - 52)