derivative of 13/3 x^3+21/2 x^2-10x-7

Lösung

\frac{d}{d x} (\frac{13}{3} x^{3} + \frac{21}{2} x^{2} - 10 x - 7)

13 x^{2} + 21 x - 10

Schritte zur Lösung

\frac{d}{d x} (\frac{13}{3} x^{3} + \frac{21}{2} x^{2} - 10 x - 7)

Vereinfache

\frac{13}{3} x^{3} + \frac{21}{2} x^{2} - 10 x - 7 : \frac{13 x ^{3}}{3} + \frac{21 x ^{2}}{2} - 10 x - 7

= \frac{d}{d x} (\frac{13 x ^{3}}{3} + \frac{21 x ^{2}}{2} - 10 x - 7)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{13 x ^{3}}{3}) + \frac{d}{d x} (\frac{21 x ^{2}}{2}) - \frac{d}{d x} (10 x) - \frac{d}{d x} (7)

\frac{d}{d x} (\frac{13 x ^{3}}{3}) = 13 x^{2}

\frac{d}{d x} (\frac{21 x ^{2}}{2}) = 21 x

\frac{d}{d x} (10 x) = 10

\frac{d}{d x} (7) = 0

= 13 x^{2} + 21 x - 10 - 0

Vereinfache

= 13 x^{2} + 21 x - 10

\int \frac{x ^{2}}{3 + 1} d x

t an g e n t f (x) = sin (sin (x)), (3 π, 0)

d er i v a t i v e f (x) = x - 3

\int 2 y x d x

\frac{d}{d x} (\frac{x + 1}{x ^{2} - 3})