derivative of ax^n+cy(x^n)

Lösung

\frac{d}{d x} (a x^{n} + c y (x) (x)^{n})

an x^{n - 1} + c (\frac{d}{d x} (y (x)) x^{n} + n x^{n - 1} y (x))

Schritte zur Lösung

\frac{d}{d x} (a x^{n} + c y (x) (x)^{n})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (a x^{n}) + \frac{d}{d x} (c y (x) x^{n})

\frac{d}{d x} (a x^{n}) = an x^{n - 1}

\frac{d}{d x} (c y (x) x^{n}) = c (\frac{d}{d x} (y (x)) x^{n} + n x^{n - 1} y (x))

= an x^{n - 1} + c (\frac{d}{d x} (y (x)) x^{n} + n x^{n - 1} y (x))

d er i v a t i v e \frac{x}{3 1 + x ^{2}}

d er i v a t i v e \frac{6 x}{7 - tan ( x )}

d er i v a t i v e - x^{2} + 260 x

\int \frac{1}{( x - 2 ) ( x - 3 ) ( x - 4 )} d x

x \to 2 lim (\frac{5}{( x - 2 ) ^{2}})