derivative of x/(x-3-arcsec(2x))

Lösung

\frac{d}{d x} (\frac{x}{x - 3} - arcsec (2 x))

- \frac{3}{( x - 3 ) ^{2}} - \frac{1}{x 4 x ^{2} - 1}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x - 3} - arcsec (2 x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x}{x - 3}) - \frac{d}{d x} (arcsec (2 x))

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

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

= - \frac{3}{( x - 3 ) ^{2}} - \frac{1}{x 4 x ^{2} - 1}

x \to 0 lim (\frac{x}{tan ( x )})

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0

\int cos^{2} (x) sin^{2} (x) d x

(2 y^{2} + 3 x y) + (2 x y + x^{2}) y^{^{'}} = 0

x^{^{''}} + 9 x = 0, x (0) = 0.7, x^{^{'}} (0) = 0.4