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

解答

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

- sin (2 x)

求解步骤

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

化简

\frac{1 + cos ( 2 x )}{2} : cos^{2} (x)

= \frac{d}{d x} (cos^{2} (x))

使用连锁律:

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

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

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

= 2 cos (x) (- sin (x))

化简

2 cos (x) (- sin (x)) : - sin (2 x)

= - sin (2 x)

\int ln ∣ e^{x y} cos (x) ∣ d y

\int t \cdot ln (t + 1) d t

\frac{d}{d x} (\frac{3}{x + 9})

\frac{\partial}{\partial x} (\frac{( x ^{2} )}{y + 3})

x \to 4 lim (\frac{∣ x ∣ - 4}{x - 4})