derivative log_{e}(sin(2x)+cot(2x))

Lösung

ableitung von

lo g_{e} (sin (2 x) + cot (2 x))

\frac{2 cos ( 2 x ) - 2 csc ^{2} ( 2 x )}{sin ( 2 x ) + cot ( 2 x )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{e} (sin (2 x) + cot (2 x)))

Vereinfache

lo g_{e} (sin (2 x) + cot (2 x)) : ln (sin (2 x) + cot (2 x))

= \frac{d}{d x} (ln (sin (2 x) + cot (2 x)))

Wende die Kettenregel an:

\frac{1}{sin ( 2 x ) + cot ( 2 x )} \frac{d}{d x} (sin (2 x) + cot (2 x))

= \frac{1}{sin ( 2 x ) + cot ( 2 x )} \frac{d}{d x} (sin (2 x) + cot (2 x))

\frac{d}{d x} (sin (2 x) + cot (2 x)) = cos (2 x) \cdot 2 - csc^{2} (2 x) \cdot 2

= \frac{1}{sin ( 2 x ) + cot ( 2 x )} (cos (2 x) \cdot 2 - csc^{2} (2 x) \cdot 2)

Vereinfache

\frac{1}{sin ( 2 x ) + cot ( 2 x )} (cos (2 x) \cdot 2 - csc^{2} (2 x) \cdot 2) : \frac{2 cos ( 2 x ) - 2 csc ^{2} ( 2 x )}{sin ( 2 x ) + cot ( 2 x )}

= \frac{2 cos ( 2 x ) - 2 csc ^{2} ( 2 x )}{sin ( 2 x ) + cot ( 2 x )}

d er i v a t i v e y = \frac{1}{2} x

\int_{π}^{2 π} (t - π) e^{- s t} d t

d er i v a t i v e 13 - x^{2}

\frac{\partial}{\partial y} (3 arctan (\frac{x}{y}))

\frac{\partial}{\partial y} (- sin (x y) y)