derivative of log_{e}(cos(4x))

Lösung

\frac{d}{d x} (lo g_{e} (cos (4 x)))

- 4 tan (4 x)

Schritte zur Lösung

\frac{d}{d x} (lo g_{e} (cos (4 x)))

Vereinfache

lo g_{e} (cos (4 x)) : ln (cos (4 x))

= \frac{d}{d x} (ln (cos (4 x)))

Wende die Kettenregel an:

\frac{1}{cos ( 4 x )} \frac{d}{d x} (cos (4 x))

= \frac{1}{cos ( 4 x )} \frac{d}{d x} (cos (4 x))

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= \frac{1}{cos ( 4 x )} (- sin (4 x) \cdot 4)

Vereinfache

\frac{1}{cos ( 4 x )} (- sin (4 x) \cdot 4) : - 4 tan (4 x)

= - 4 tan (4 x)

\int x ln (x^{5}) d x

\int_{0}^{\frac{π}{4}} x sin (2 x) d x

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\int e^{2 x} cos (7 x) d x

z \to 1 - i lim (x + i (2 x + y))