derivative of sin((sqrt(5)/2 ln(x)))

解答

\frac{d}{d x} (sin (\frac{5}{2} ln (x)))

\frac{5 cos ( \frac{5}{2} ln ( x ) )}{2 x}

求解步骤

\frac{d}{d x} (sin (\frac{5}{2} ln (x)))

使用连锁律:

cos (\frac{5}{2} ln (x)) \frac{d}{d x} (\frac{5}{2} ln (x))

= cos (\frac{5}{2} ln (x)) \frac{d}{d x} (\frac{5}{2} ln (x))

\frac{d}{d x} (\frac{5}{2} ln (x)) = \frac{5}{2 x}

= cos (\frac{5}{2} ln (x)) \frac{5}{2 x}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 cos ( \frac{5}{2} ln ( x ) )}{2 x}

\int \frac{sin ( k t )}{a + cos ( k t )} d t

x \to 3 lim (3 x^{2} + 4 x - 1)

x \to 0 lim (\frac{x - 2}{x - 2})

\frac{\partial}{\partial y} (e^{- x} sin (y))

\frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2} - 9)