derivative of sqrt((1+cos(x)/2))

解答

\frac{d}{d x} (\frac{1 + cos ( x )}{2})

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

求解步骤

\frac{d}{d x} (\frac{1 + cos ( x )}{2})

使用连锁律:

\frac{1}{2 \frac{1 + c o s ( x )}{2}} \frac{d}{d x} (\frac{1 + cos ( x )}{2})

= \frac{1}{2 \frac{1 + c o s ( x )}{2}} \frac{d}{d x} (\frac{1 + cos ( x )}{2})

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

= \frac{1}{2 \frac{1 + c o s ( x )}{2}} (- \frac{1}{2} sin (x))

化简

\frac{1}{2 \frac{1 + c o s ( x )}{2}} (- \frac{1}{2} sin (x)) : - \frac{sin ( x )}{2 2 1 + cos ( x )}

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

\int e^{x} sin (6 x) d x

\frac{d}{d x} (\frac{x ^{3} + 2}{3})

\int e^{6 x} cos (2 x) d x

\frac{d}{d x} (\frac{4}{4 x})

y^{^{''}} + 2 y^{^{'}} + 1 y = 0