derivative of tan^2(x/2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} ((2 x - 5)^{2})

\int \frac{x ^{3}}{2 x - 1} d x

x \to 0 lim (∣ x ∣^{x})

x \to 3 - lim (\frac{6}{( x - 3 ) ^{5}})

a re a y = x^{2}, y = 3 - 2 x