derivative of (tan(x)^{1/2})

Lösung

\frac{d}{d x} ((tan (x))^{\frac{1}{2}})

\frac{sec ^{2} ( x )}{2 tan ^{\frac{1}{2}} ( x )}

Schritte zur Lösung

\frac{d}{d x} ((tan (x))^{\frac{1}{2}})

Wende die Kettenregel an:

\frac{1}{2 tan ^{\frac{1}{2}} ( x )} \frac{d}{d x} (tan (x))

= \frac{1}{2 tan ^{\frac{1}{2}} ( x )} \frac{d}{d x} (tan (x))

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= \frac{1}{2 tan ^{\frac{1}{2}} ( x )} sec^{2} (x)

Vereinfache

\frac{1}{2 tan ^{\frac{1}{2}} ( x )} sec^{2} (x) : \frac{sec ^{2} ( x )}{2 tan ^{\frac{1}{2}} ( x )}

= \frac{sec ^{2} ( x )}{2 tan ^{\frac{1}{2}} ( x )}

\int_{0}^{l n (3)} e^{x} d x

\int e^{c o s (40 t)} sin (40 t) d t

\frac{d}{d x} (\frac{6 x}{x ^{2} + 36})

l a pl a ce t r an s f or m e^{- 3}

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