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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= \frac{1}{5} (3 x^{2} - 2 x + 0)

Vereinfache

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

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

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

s im pl i f y lo g_{10} (\frac{( x + 1 ) ( x - 8 )}{( x - 1 ) ( x + 8 )})

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

\frac{\partial}{\partial x} (e^{8 x y})