derivative of 1/8 x-ln(2x)

解答

\frac{d}{d x} (\frac{1}{8} x - ln (2 x))

\frac{1}{8} - \frac{1}{x}

求解步骤

\frac{d}{d x} (\frac{1}{8} x - ln (2 x))

化简

\frac{1}{8} x - ln (2 x) : \frac{x}{8} - ln (2 x)

= \frac{d}{d x} (\frac{x}{8} - ln (2 x))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x}{8}) - \frac{d}{d x} (ln (2 x))

\frac{d}{d x} (\frac{x}{8}) = \frac{1}{8}

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

= \frac{1}{8} - \frac{1}{x}

d er i v a t i v e f (x) = 5 x ln (x)

\frac{d}{d x} (- 3 x^{5} + 5 x^{3})

d er i v a t i v e y = t^{3} - 2 t + 4

x \to 0 lim (\frac{( 2 + x ) ^{2} + 4}{x})

d er i v a t i v e \frac{1}{x ( 5 + ln ( x ) )}