derivative of 3/(sin(x+cos(x)))

Lösung

\frac{d}{d x} (\frac{3}{sin ( x ) + cos ( x )})

- \frac{3 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{sin ( x ) + cos ( x )})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (\frac{1}{sin ( x ) + cos ( x )})

Wende Exponentenregel an:

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

= 3 \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)

= 3 (- \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} (cos (x) - sin (x)))

Vereinfache

3 (- \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} (cos (x) - sin (x))) : - \frac{3 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

= - \frac{3 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

\int \frac{x ^{2}}{3 1 + x ^{3}} d x

x \to 0 lim (cot (2 x))

\int (x - 5) sin (π x) d x

\frac{\partial}{\partial x} (- \frac{8 x}{y})

\frac{d}{d x} (\frac{1}{7 x})