derivative of arctan(sin(x^2+pi/x))

Lösung

\frac{d}{d x} (arctan (sin (x^{2} + \frac{π}{x})))

\frac{cos ( \frac{x ^{3} + π}{x} ) ( 2 x ^{3} - π )}{x ^{2} ( sin ^{2} ( x ^{2} + \frac{π}{x} ) + 1 )}

Schritte zur Lösung

\frac{d}{d x} (arctan (sin (x^{2} + \frac{π}{x})))

Wende die Kettenregel an:

\frac{1}{( sin ( x ^{2} + \frac{π}{x} ) ) ^{2} + 1} \frac{d}{d x} (sin (x^{2} + \frac{π}{x}))

= \frac{1}{( sin ( x ^{2} + \frac{π}{x} ) ) ^{2} + 1} \frac{d}{d x} (sin (x^{2} + \frac{π}{x}))

\frac{d}{d x} (sin (x^{2} + \frac{π}{x})) = cos (x^{2} + \frac{π}{x}) (2 x - \frac{π}{x ^{2}})

= \frac{1}{( sin ( x ^{2} + \frac{π}{x} ) ) ^{2} + 1} cos (x^{2} + \frac{π}{x}) (2 x - \frac{π}{x ^{2}})

Vereinfache

\frac{1}{sin ^{2} ( x ^{2} + \frac{π}{x} ) + 1} cos (x^{2} + \frac{π}{x}) (2 x - \frac{π}{x ^{2}}) : \frac{cos ( \frac{x ^{3} + π}{x} ) ( 2 x ^{3} - π )}{x ^{2} ( sin ^{2} ( x ^{2} + \frac{π}{x} ) + 1 )}

= \frac{cos ( \frac{x ^{3} + π}{x} ) ( 2 x ^{3} - π )}{x ^{2} ( sin ^{2} ( x ^{2} + \frac{π}{x} ) + 1 )}

y^{^{''}} + y^{^{'}} + y = t

\frac{d}{d x} (6 x^{2} - 4 x)

y^{^{''}} + 5 y = 0, y^{^{'}} (1) = 5

d er i v a t i v e - \frac{1}{4 x ^{\frac{3}{2}}}

y^{^{''}} + 8 y^{^{'}} + 20 y = 0