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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{sec ^{2} ( \frac{x}{2} )}{6 ( tan ( \frac{x}{2} ) - 3 )}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

\frac{1}{\frac{t a n ( \frac{x}{2} ) - 3}{3}} \frac{d}{d x} (\frac{tan ( \frac{x}{2} ) - 3}{3})

= \frac{1}{\frac{t a n ( \frac{x}{2} ) - 3}{3}} \frac{d}{d x} (\frac{tan ( \frac{x}{2} ) - 3}{3})

\frac{d}{d x} (\frac{tan ( \frac{x}{2} ) - 3}{3}) = \frac{1}{6} sec^{2} (\frac{x}{2})

= - \frac{1}{3} \cdot \frac{1}{\frac{t a n ( \frac{x}{2} ) - 3}{3}} \cdot \frac{1}{6} sec^{2} (\frac{x}{2})

Vereinfache

- \frac{1}{3} \cdot \frac{1}{\frac{t a n ( \frac{x}{2} ) - 3}{3}} \cdot \frac{1}{6} sec^{2} (\frac{x}{2}) : - \frac{sec ^{2} ( \frac{x}{2} )}{6 ( tan ( \frac{x}{2} ) - 3 )}

= - \frac{sec ^{2} ( \frac{x}{2} )}{6 ( tan ( \frac{x}{2} ) - 3 )}

Graph

Beliebte Beispiele

y^{''}+6y^'+8y=130cos(3t)

y^{^{''}} + 6 y^{^{'}} + 8 y = 130 cos (3 t)

limit as x approaches-1/e of xln(e+1/x)

x \to - \frac{1}{e} lim (x ln (e + \frac{1}{x}))

integral of xsqrt(1-2x)

\int x 1 - 2 x d x

(\partial)/(\partial x)(x/(e^{x/y)})

\frac{\partial}{\partial x} (\frac{x}{e ^{\frac{x}{y}}})

derivative of-2/((6x-7x^4^3))

\frac{d}{d x} (- \frac{2}{( 6 x - 7 x ^{4} ) ^{3}})