derivative of arcsin(sqrt(sin(13x)))

解答

\frac{d}{d x} (arcsin (sin (13 x)))

\frac{13 cos ( 13 x )}{2 sin ( 13 x ) 1 - sin ( 13 x )}

求解步骤

\frac{d}{d x} (arcsin (sin (13 x)))

使用连锁律:

\frac{1}{1 - ( sin ( 13 x ) ) ^{2}} \frac{d}{d x} (sin (13 x))

= \frac{1}{1 - ( sin ( 13 x ) ) ^{2}} \frac{d}{d x} (sin (13 x))

\frac{d}{d x} (sin (13 x)) = \frac{13 cos ( 13 x )}{2 sin ( 13 x )}

= \frac{1}{1 - ( sin ( 13 x ) ) ^{2}} \cdot \frac{13 cos ( 13 x )}{2 sin ( 13 x )}

化简

\frac{1}{1 - ( sin ( 13 x ) ) ^{2}} \cdot \frac{13 cos ( 13 x )}{2 sin ( 13 x )} : \frac{13 cos ( 13 x )}{2 sin ( 13 x ) 1 - sin ( 13 x )}

= \frac{13 cos ( 13 x )}{2 sin ( 13 x ) 1 - sin ( 13 x )}

\frac{d}{d x} (\frac{1}{4 - 3 x})

s im pl i f y - \frac{x}{y}

\int sin (x) 1 + cos^{2} (x) d x

\frac{d P}{d t} = P (1 0^{- 1} - P \cdot 1 0^{- 7}), P (0) = 7000

d er i v a t i v e f (x) = x^{- \frac{1}{2}}