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

Lösung

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

x^{4} - 6 x^{2} + 3

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (\frac{x ^{5}}{5}) = x^{4}

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

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

= x^{4} - 6 x^{2} + 3

x \to - 1 lim (6 x + 3)

x \to 1 lim (\frac{e ^{x}}{1 - x})

x \to 1 lim (\frac{1 ( x )}{1 - 3 x})

s \to 0 lim (\frac{1}{s})

\int_{0}^{1} 2 π (2 - y) (7 y^{2}) d y