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Beliebt Rechnen >

derivative of ln(1+sin(x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of (f(x(6x))^2-2)

\frac{d}{d x} ((f (x) (6 x))^{2} - 2)

limit as x approaches 0+of 2+ln(x)

x \to 0 + lim (2 + ln (x))

derivative sin(x)*tan(x)

d er i v a t i v e sin (x) \cdot tan (x)

fläche f(x)=x^5+4,g(x)=x+4

a re a f (x) = x^{5} + 4, g (x) = x + 4

tangent f(x)=-1/(2sqrt(1-x)),\at x=-8

t an g e n t f (x) = - \frac{1}{2 1 - x}, at x = - 8