derivative of 5/3 x^3+x^2-1

Lösung

\frac{d}{d x} (\frac{5}{3} x^{3} + x^{2} - 1)

5 x^{2} + 2 x

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{3} x^{3} + x^{2} - 1)

Vereinfache

\frac{5}{3} x^{3} + x^{2} - 1 : \frac{5 x ^{3}}{3} + x^{2} - 1

= \frac{d}{d x} (\frac{5 x ^{3}}{3} + x^{2} - 1)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{5 x ^{3}}{3}) + \frac{d}{d x} (x^{2}) - \frac{d}{d x} (1)

\frac{d}{d x} (\frac{5 x ^{3}}{3}) = 5 x^{2}

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

\frac{d}{d x} (1) = 0

= 5 x^{2} + 2 x - 0

Vereinfache

= 5 x^{2} + 2 x

\int \frac{sin ^{7} ( ln ( x ) )}{x} d x

\frac{1}{x ^{8}} y^{^{'}} = 12 + 15 y

\frac{\partial}{\partial x} (x^{2} y + x y^{2})

t an g e n t y = x^{3}, at x = - 9

d er i v a t i v e (1 + sin (x))^{- 4}