derivative of 4/3 x^3-4x^2-60x+10

Lösung

\frac{d}{d x} (\frac{4}{3} x^{3} - 4 x^{2} - 60 x + 10)

4 x^{2} - 8 x - 60

Schritte zur Lösung

\frac{d}{d x} (\frac{4}{3} x^{3} - 4 x^{2} - 60 x + 10)

Vereinfache

\frac{4}{3} x^{3} - 4 x^{2} - 60 x + 10 : \frac{4 x ^{3}}{3} - 4 x^{2} - 60 x + 10

= \frac{d}{d x} (\frac{4 x ^{3}}{3} - 4 x^{2} - 60 x + 10)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{4 x ^{3}}{3}) - \frac{d}{d x} (4 x^{2}) - \frac{d}{d x} (60 x) + \frac{d}{d x} (10)

\frac{d}{d x} (\frac{4 x ^{3}}{3}) = 4 x^{2}

\frac{d}{d x} (4 x^{2}) = 8 x

\frac{d}{d x} (60 x) = 60

\frac{d}{d x} (10) = 0

= 4 x^{2} - 8 x - 60 + 0

Vereinfache

= 4 x^{2} - 8 x - 60

a re a x^{\frac{1}{4}}, 2 - x, 0

t an g e n t f (x) = x^{3} - 3 x^{2} + 1, at x = 2

\int \frac{ln ( ln ( x ) )}{x} d x

roo t s π r^{2} h

\int x^{3} - 4 x d x