d/(du)(u^2+v^2)

Lösung

\frac{d}{d u} (u^{2} + v^{2})

2 u

Schritte zur Lösung

\frac{d}{d u} (u^{2} + v^{2})

Behandle

v

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d u} (u^{2}) + \frac{d}{d u} (v^{2})

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

\frac{d}{d u} (v^{2}) = 0

= 2 u + 0

Vereinfache

= 2 u

im pl i c i t \frac{d y}{d x}, 3 x^{2} y^{3} = 3 x - 2 y^{2} - 16

d er i v a t i v e (x - 3)^{\frac{2}{3}}

y^{^{'}} = \frac{6 x}{y}

d er i v a t i v e [x + (x + sin^{2} (x))^{4}]^{3}

\int \frac{3 x ^{2} + x + 4}{x ^{4} + 3 x ^{2} + 2} d x