derivative of x^3+(4x^2/3-2x+5)

Lösung

\frac{d}{d x} (x^{3} + \frac{4 x ^{2}}{3} - 2 x + 5)

3 x^{2} + \frac{8 x}{3} - 2

Schritte zur Lösung

\frac{d}{d x} (x^{3} + \frac{4 x ^{2}}{3} - 2 x + 5)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (\frac{4 x ^{2}}{3}) - \frac{d}{d x} (2 x) + \frac{d}{d x} (5)

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

\frac{d}{d x} (\frac{4 x ^{2}}{3}) = \frac{8 x}{3}

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

\frac{d}{d x} (5) = 0

= 3 x^{2} + \frac{8 x}{3} - 2 + 0

Vereinfache

= 3 x^{2} + \frac{8 x}{3} - 2

\int e^{2 x} \cdot 2 d x

\int \frac{6}{x ( x - 6 ) ^{2}} d x

y^{^{''}} + 4 y^{^{'}} + 5 y = 15 x + 3 e^{- x}

y^{^{''}} + 8 y^{^{'}} + 7 y = - 8 - x + 24 x^{2} + 7 x^{3}

\int x^{2} \cdot 1 - x^{2} d x