derivative of ln(sqrt(3x))

解答

\frac{d}{d x} (ln (3 x))

\frac{1}{2 x}

求解步骤

\frac{d}{d x} (ln (3 x))

化简

ln (3 x) : ln (3 x)

= \frac{d}{d x} (ln (3 x))

使用连锁律:

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

= \frac{1}{3 x} \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = \frac{3}{2 x}

= \frac{1}{3 x} \cdot \frac{3}{2 x}

化简

\frac{1}{3 x} \cdot \frac{3}{2 x} : \frac{1}{2 x}

= \frac{1}{2 x}

\int_{- 1}^{0} \frac{6}{1 + ( 2 x + 1 ) ^{2}} d x

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

\int e^{a x} sin (b x) d x

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

n = 1 \sum \infty \frac{3 n}{6 n + 13}