derivative of (25x^3/3+10x^2+4x-7)

Lösung

\frac{d}{d x} (\frac{25 x ^{3}}{3} + 10 x^{2} + 4 x - 7)

25 x^{2} + 20 x + 4

Schritte zur Lösung

\frac{d}{d x} (\frac{25 x ^{3}}{3} + 10 x^{2} + 4 x - 7)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{25 x ^{3}}{3}) + \frac{d}{d x} (10 x^{2}) + \frac{d}{d x} (4 x) - \frac{d}{d x} (7)

\frac{d}{d x} (\frac{25 x ^{3}}{3}) = 25 x^{2}

\frac{d}{d x} (10 x^{2}) = 20 x

\frac{d}{d x} (4 x) = 4

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

= 25 x^{2} + 20 x + 4 - 0

Vereinfache

= 25 x^{2} + 20 x + 4

f^{^{'}} (x) = e^{- 2 x}

\frac{d}{d x} (\frac{2 x + sin ( x )}{2 x + cos ( x )})

s l o p e (1, 10), (24, - 26)

x \to 4 - lim (5 - x)

\frac{\partial}{\partial x} (\frac{1}{i} + \frac{1}{o})