derivative of-1/(x^4-5/(x^2))

Lösung

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

\frac{4}{x ^{5}} + \frac{10}{x ^{3}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (\frac{1}{x ^{4}}) - \frac{d}{d x} (\frac{5}{x ^{2}})

\frac{d}{d x} (\frac{1}{x ^{4}}) = - \frac{4}{x ^{5}}

\frac{d}{d x} (\frac{5}{x ^{2}}) = - \frac{10}{x ^{3}}

= - (- \frac{4}{x ^{5}}) - (- \frac{10}{x ^{3}})

Vereinfache

= \frac{4}{x ^{5}} + \frac{10}{x ^{3}}

a re a 4 x^{4} - 3 x^{2}, 6 x^{2}

\frac{\partial}{\partial x} (x^{2} y^{3} sin (x z))

d er i v a t i v e f (x) = x^{9} arccos (x)

\int - 3 x cos (2 x) d x

\int 2 x^{3} - \frac{2}{3} x^{2} + 5 x d x