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

Lösung

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

x^{2} + \frac{15}{x ^{6}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (\frac{3}{x ^{5}}) = - \frac{15}{x ^{6}}

\frac{d}{d x} (4 π) = 0

= x^{2} - (- \frac{15}{x ^{6}}) + 0

Vereinfache

= x^{2} + \frac{15}{x ^{6}}

\frac{d y}{d x} = \frac{( 4 y lo g _{e} ( x ) )}{x}

t an g e n t - 3 cos (x), at x = \frac{π}{2}

y^{^{''}} - 14 y^{^{'}} + 49 y = e^{8 x} (x^{2} - 9 x - 2)

y^{^{'}} = 1 + e^{y - x + 5}

\int (x^{2} - 4)^{2} (2 x) d x