derivative of cos(arctan(5x))

Lösung

\frac{d}{d x} (cos (arctan (5 x)))

- \frac{25 x}{( 25 x ^{2} + 1 ) 1 + 25 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (cos (arctan (5 x)))

Wende die Kettenregel an:

- sin (arctan (5 x)) \frac{d}{d x} (arctan (5 x))

= - sin (arctan (5 x)) \frac{d}{d x} (arctan (5 x))

\frac{d}{d x} (arctan (5 x)) = \frac{5}{25 x ^{2} + 1}

= - sin (arctan (5 x)) \frac{5}{25 x ^{2} + 1}

Vereinfache

- sin (arctan (5 x)) \frac{5}{25 x ^{2} + 1} : - \frac{25 x}{( 25 x ^{2} + 1 ) 1 + 25 x ^{2}}

= - \frac{25 x}{( 25 x ^{2} + 1 ) 1 + 25 x ^{2}}

n = 0 \sum \infty n^{n} (x - 3)^{n}

x \to 2 lim (\frac{3}{x + 2})

in v erse l a pl a ce \frac{s}{( s - 2 ) ( s - 3 ) ( s - 6 )}

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

d er i v a t i v e y = (5 x + 1)^{3} (x - 4)