derivative of (x^3-y^3/(x-y))

Lösung

\frac{d}{d x} (\frac{x ^{3} - y ^{3}}{x - y})

2 x + y + x \frac{d y}{d x} + 2 y \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3} - y ^{3}}{x - y})

Vereinfache

\frac{x ^{3} - y ^{3}}{x - y} : x^{2} + x y + y^{2}

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

= 2 x + y + x \frac{d y}{d x} + 2 y \frac{d y}{d x}

x \to 0 lim (+ (x^{x}))

y^{^{'}} = 7 t y^{2}

d er i v a t i v e \frac{ln ( x )}{x ^{5}}

θ \to 0 lim (\frac{sin ( 7 θ )}{θ})

d er i v a t i v e x^{2} - 5 x + 9