derivative f(x)=ln(5x)

解答

导数

f (x) = ln (5 x)

\frac{1}{x}

求解步骤

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

使用连锁律:

\frac{1}{5 x} \frac{d}{d x} (5 x)

= \frac{1}{5 x} \frac{d}{d x} (5 x)

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

= \frac{1}{5 x} \cdot 5

化简

\frac{1}{5 x} \cdot 5 : \frac{1}{x}

= \frac{1}{x}

x \to \infty lim (x \cdot 5)

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

y^{^{'}} = \frac{( 1 + x )}{x y ^{4}}, y (1) = 3

\frac{d}{d x} (- 2 x - y^{2} cos (x y^{2}) - 1)

\int \frac{4 x + 1}{4 x ^{2} + 2 x + 3} d x