derivative of 7/(sin(x+cos(x)))

Lösung

\frac{d}{d x} (\frac{7}{sin ( x ) + cos ( x )})

- \frac{7 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{7}{sin ( x ) + cos ( x )})

Entferne die Konstante:

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

= 7 \frac{d}{d x} (\frac{1}{sin ( x ) + cos ( x )})

Wende Exponentenregel an:

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

= 7 \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)

= 7 (- \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} (cos (x) - sin (x)))

Vereinfache

7 (- \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} (cos (x) - sin (x))) : - \frac{7 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

= - \frac{7 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

\int sin^{4} (x) cos^{7} (x) d x

\int 4 x - 11 d x

y^{^{'}} = e^{4 c o s (x)}

l a pl a ce t r an s f or m 2

x \to 6 - lim (36 - x^{2})