derivative 9/(sin(x)+cos(x))

Lösung

ableitung von

\frac{9}{sin ( x ) + cos ( x )}

- \frac{9 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{9}{sin ( x ) + cos ( x )})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (\frac{1}{sin ( x ) + cos ( x )})

Wende Exponentenregel an:

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

= 9 \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)

= 9 (- \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} (cos (x) - sin (x)))

Vereinfache

9 (- \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} (cos (x) - sin (x))) : - \frac{9 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

= - \frac{9 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

\frac{d}{d x} (\frac{3 x}{8})

\frac{\partial}{\partial s} (r ln (r^{2} + s^{2}))

\frac{d}{d x} (\frac{80}{x})

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{x} (1 - x)

t a y l or 5 x e^{x}