derivative of (1/2 ^{sqrt(sin^2(x))})

Lösung

\frac{d}{d x} (\frac{1}{2})^{s i n^{2} (x)}

- \frac{ln ( 2 ) sin ( 2 x )}{2 ^{s i n (x) + 1} sin ( x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2})^{s i n^{2} (x)}

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

(\frac{1}{2})^{s i n^{2} (x)} = e^{s i n^{2} (x) l n (\frac{1}{2})}

= \frac{d}{d x} (e^{s i n^{2} (x) l n (\frac{1}{2})})

Wende die Kettenregel an:

e^{s i n^{2} (x) l n (\frac{1}{2})} \frac{d}{d x} (sin^{2} (x) ln (\frac{1}{2}))

= e^{s i n^{2} (x) l n (\frac{1}{2})} \frac{d}{d x} (sin^{2} (x) ln (\frac{1}{2}))

\frac{d}{d x} (sin^{2} (x) ln (\frac{1}{2})) = - \frac{ln ( 2 ) sin ( 2 x )}{2 sin ^{2} ( x )}

= e^{s i n^{2} (x) l n (\frac{1}{2})} - \frac{ln ( 2 ) sin ( 2 x )}{2 sin ^{2} ( x )}

Vereinfache

e^{s i n^{2} (x) l n (\frac{1}{2})} - \frac{ln ( 2 ) sin ( 2 x )}{2 sin ^{2} ( x )} : - \frac{ln ( 2 ) sin ( 2 x )}{2 ^{s i n (x) + 1} sin ( x )}

= - \frac{ln ( 2 ) sin ( 2 x )}{2 ^{s i n (x) + 1} sin ( x )}

\frac{d}{d x} (\frac{1}{( 2 - x )})

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

x^{2} + y^{2} + 2 x y y^{^{'}} = 0

\int (x + 1) e^{- 2 x} d x

d er i v a t i v e f (x) = \frac{x ^{2} - 2 x - 3}{x}