derivative of ln(sin(x+cos(x)))

Lösung

\frac{d}{d x} (ln (sin (x) + cos (x)))

\frac{cos ( x ) - sin ( x )}{sin ( x ) + cos ( x )}

Schritte zur Lösung

\frac{d}{d x} (ln (sin (x) + cos (x)))

Wende die Kettenregel an:

\frac{1}{sin ( x ) + cos ( x )} \frac{d}{d x} (sin (x) + cos (x))

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

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

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

Vereinfache

\frac{1}{sin ( x ) + cos ( x )} (cos (x) - sin (x)) : \frac{cos ( x ) - sin ( x )}{sin ( x ) + cos ( x )}

= \frac{cos ( x ) - sin ( x )}{sin ( x ) + cos ( x )}

\int - x^{2} + 6 x d x

\int sin^{3} (2 θ) cot (2 θ) d θ

x \to \infty lim (\frac{3 x + 5 x + 3}{- 2 x + x ^{\frac{2}{3}} + 7})

t an g e n t f (x) = 2 x^{3} - x^{2} + 2, (1, 3)

x \to - 1 + lim (f (x))