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Beliebt Rechnen >

derivative g(x)=(sin(8x))/(cos(x))

Lösung

ableitung von

g (x) = \frac{sin ( 8 x )}{cos ( x )}

Lösung

cos (8 x) \cdot 8 sec (x) + sec (x) tan (x) sin (8 x)

Schritte zur Lösung

\frac{d}{d x} (\frac{sin ( 8 x )}{cos ( x )})

Vereinfache

\frac{sin ( 8 x )}{cos ( x )} : sin (8 x) sec (x)

= \frac{d}{d x} (sin (8 x) sec (x))

Wende die Produktregel an:

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

f = sin (8 x), g = sec (x)

= \frac{d}{d x} (sin (8 x)) sec (x) + \frac{d}{d x} (sec (x)) sin (8 x)

\frac{d}{d x} (sin (8 x)) = cos (8 x) \cdot 8

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

= cos (8 x) \cdot 8 sec (x) + sec (x) tan (x) sin (8 x)

Graph

Beliebte Beispiele

integral from 1 to infinity of-1/x

\int_{1}^{\infty} - \frac{1}{x} d x

(cos(3x))y^'-3(tan(3x))y=-10sec(3x)

(cos (3 x)) y^{^{'}} - 3 (tan (3 x)) y = - 10 sec (3 x)

derivative (t+1)cos(-t)

d er i v a t i v e (t + 1) cos (- t)

integral of-2cos^2(x)sin(x)

\int - 2 cos^{2} (x) sin (x) d x

(dv)/(dt)=32-4/5 v

\frac{d v}{d t} = 32 - \frac{4}{5} v