derivative of-3/2 x^5+2/5 x^3-1/6 x^2-4x

Lösung

\frac{d}{d x} (- \frac{3}{2} x^{5} + \frac{2}{5} x^{3} - \frac{1}{6} x^{2} - 4 x)

- \frac{15 x ^{4}}{2} + \frac{6 x ^{2}}{5} - \frac{x}{3} - 4

Schritte zur Lösung

\frac{d}{d x} (- \frac{3}{2} x^{5} + \frac{2}{5} x^{3} - \frac{1}{6} x^{2} - 4 x)

Vereinfache

- \frac{3}{2} x^{5} + \frac{2}{5} x^{3} - \frac{1}{6} x^{2} - 4 x : - \frac{3 x ^{5}}{2} + \frac{2 x ^{3}}{5} - \frac{x ^{2}}{6} - 4 x

= \frac{d}{d x} (- \frac{3 x ^{5}}{2} + \frac{2 x ^{3}}{5} - \frac{x ^{2}}{6} - 4 x)

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (\frac{3 x ^{5}}{2}) + \frac{d}{d x} (\frac{2 x ^{3}}{5}) - \frac{d}{d x} (\frac{x ^{2}}{6}) - \frac{d}{d x} (4 x)

\frac{d}{d x} (\frac{3 x ^{5}}{2}) = \frac{15 x ^{4}}{2}

\frac{d}{d x} (\frac{2 x ^{3}}{5}) = \frac{6 x ^{2}}{5}

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

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

= - \frac{15 x ^{4}}{2} + \frac{6 x ^{2}}{5} - \frac{x}{3} - 4

d er i v a t i v e y = ln (\frac{x}{5 - x})

x \to \infty lim (3 - x^{2})

\frac{d}{d x} (\frac{x - 6}{x + 6})

f (θ) = 13 θ - 8 sin (θ)

\int \frac{1}{a s} d s