derivative of 1/(sin(x+cos(x)))

Lösung

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

- \frac{cos ( x ) - sin ( x )}{1 + sin ( 2 x )}

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

- \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} \frac{d}{d x} (sin (x) + cos (x))

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

Vereinfache

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

= - \frac{cos ( x ) - sin ( x )}{1 + sin ( 2 x )}

a re a y = x^{2} + 2, y = - x, x = 0, x = 1

\int \frac{29}{( x + 1 ) ( x ^{2} + x )} d x

d er i v a t i v e y = \frac{e ^{x}}{9 x ^{2}}

\int \frac{( x ^{2} )}{13 - 4 x + x ^{2}} d x

\frac{d}{d x} (\frac{x + 6}{x ^{3} + x - 1})