(\partial)/(\partial x)(ax^2+by^2)

Lösung

\frac{\partial}{\partial x} (a x^{2} + b y^{2})

2 a x

Schritte zur Lösung

\frac{\partial}{\partial x} (a x^{2} + b y^{2})

Behandle

a, b, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (a x^{2}) + \frac{\partial}{\partial x} (b y^{2})

\frac{\partial}{\partial x} (a x^{2}) = 2 a x

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

= 2 a x + 0

Vereinfache

= 2 a x

\frac{d}{d x} (\frac{x}{x ^{2} + 81})

d er i v a t i v e f (x) = 3 x + \frac{8}{x ^{3}}

n = 0 \sum \infty n + (- 1)^{n}

d er i v a t i v e \frac{e ^{x} + e ^{- x}}{e ^{2 x}}

(2 x^{4})^{^{'}}