derivative of (sin(5x)/(cos(6x)))

Lösung

\frac{d}{d x} (\frac{sin ( 5 x )}{cos ( 6 x )})

cos (5 x) \cdot 5 sec (6 x) + sec (6 x) tan (6 x) \cdot 6 sin (5 x)

Schritte zur Lösung

\frac{d}{d x} (\frac{sin ( 5 x )}{cos ( 6 x )})

Vereinfache

\frac{sin ( 5 x )}{cos ( 6 x )} : sin (5 x) sec (6 x)

= \frac{d}{d x} (sin (5 x) sec (6 x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (5 x), g = sec (6 x)

= \frac{d}{d x} (sin (5 x)) sec (6 x) + \frac{d}{d x} (sec (6 x)) sin (5 x)

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

\frac{d}{d x} (sec (6 x)) = sec (6 x) tan (6 x) \cdot 6

= cos (5 x) \cdot 5 sec (6 x) + sec (6 x) tan (6 x) \cdot 6 sin (5 x)

\frac{d}{d x} ((x^{2} - 4)^{2} (x - 1))

d er i v a t i v e \frac{( 1 - 5 t )}{2 + t}

\frac{\partial}{\partial x} (\frac{1}{2 π t} e^{- \frac{( x - y ) ^{2}}{2 t}})

x \to 1 - lim (2 x - 1)

d er i v a t i v e f (x) = \frac{4 x}{x ^{2} + 4}