derivative of cos(ln(x^2))

Lösung

\frac{d}{d x} (cos (ln (x^{2})))

- \frac{2 sin ( 2 ln ( x ) )}{x}

Schritte zur Lösung

\frac{d}{d x} (cos (ln (x^{2})))

Wende die Kettenregel an:

- sin (ln (x^{2})) \frac{d}{d x} (ln (x^{2}))

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

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

= - sin (ln (x^{2})) \frac{2}{x}

Vereinfache

- sin (ln (x^{2})) \frac{2}{x} : - \frac{2 sin ( 2 ln ( x ) )}{x}

= - \frac{2 sin ( 2 ln ( x ) )}{x}

d er i v a t i v e 2 cos (3 x)

y^{^{'}} + \frac{2 x}{1 + x ^{2}} y = \frac{e ^{- x}}{1 + x ^{2}}

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

x \to \infty lim (x^{- 1})

d er i v a t i v e x^{\frac{4}{5}}