derivative of (z(x^2+z^2))

Lösung

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

x^{2} \frac{d z}{d x} + 2 x z + 3 z^{2} \frac{d z}{d x}

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = z, g = x^{2} + z^{2}

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

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

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

Vereinfache

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

= x^{2} \frac{d z}{d x} + 2 x z + 3 z^{2} \frac{d z}{d x}

e x p an d (3 x + 4 y = - 2) 5

e x p an d (x^{2} - 1) y + y^{2} (x + 1) y^{'} (x)

e x p an d 3 (8 π - \frac{64 π - 48 3}{9})

e x p an d - \frac{K}{x ( x - K )}

e x p an d 1 - cos^{2} (x)