derivative of tan(x+xsec^2(x))

Lösung

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

2 sec^{2} (x) + 2 x sec^{2} (x) tan (x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= sec^{2} (x) + sec^{2} (x) + 2 x sec^{2} (x) tan (x)

Vereinfache

= 2 sec^{2} (x) + 2 x sec^{2} (x) tan (x)

d er i v a t i v e sin (tan (x) + sec (x))

\frac{d}{d x} (cos (5 x - \frac{π}{2}))

in v erse l a pl a ce \frac{s}{s ^{2} - s + 1}

in v erse l a pl a ce \frac{3}{s ( s + 3 )}

t an g e n t x^{2} + 3 x