derivative 15x^{100}-3x^{12}+5x-46

Lösung

ableitung von

15 x^{100} - 3 x^{12} + 5 x - 46

1500 x^{99} - 36 x^{11} + 5

Schritte zur Lösung

\frac{d}{d x} (15 x^{100} - 3 x^{12} + 5 x - 46)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (15 x^{100}) - \frac{d}{d x} (3 x^{12}) + \frac{d}{d x} (5 x) - \frac{d}{d x} (46)

\frac{d}{d x} (15 x^{100}) = 1500 x^{99}

\frac{d}{d x} (3 x^{12}) = 36 x^{11}

\frac{d}{d x} (5 x) = 5

\frac{d}{d x} (46) = 0

= 1500 x^{99} - 36 x^{11} + 5 - 0

Vereinfache

= 1500 x^{99} - 36 x^{11} + 5

d er i v a t i v e \frac{- 6}{x}

d er i v a t i v e y = (\frac{x + 1}{x})^{2}

d er i v a t i v e \frac{x ^{4}}{2}

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

d er i v a t i v e 6 x^{2} + 12 x - 13