derivative of 1/3 tan^3(x/2-tan(x/2))

Lösung

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2}) - tan (\frac{x}{2}))

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2}) - tan (\frac{x}{2}))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2})) - \frac{d}{d x} (tan (\frac{x}{2}))

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2})) = \frac{1}{2} tan^{2} (\frac{x}{2}) sec^{2} (\frac{x}{2})

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

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

\frac{d}{d x} (n x^{n})

d er i v a t i v e \frac{2 x ^{2} + 8 x + 4}{x}

\frac{d}{d x} (\frac{- cos ( x ) - 1}{x ^{3} + x ^{2}})

t an g e n t y = 1 + 4 x^{2} - 2 x^{3}

\frac{\partial}{\partial y} (x^{3} - x y^{2} + 3 y^{2})