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

解答

导数

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

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

求解步骤

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

化简

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

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

使用微分乘法定则:

(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)

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

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

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

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

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