derivative of ln(4log_{4}(x)+pi^3)

解

\frac{d}{d x} (ln (4) lo g_{4} (x) + π^{3})

\frac{1}{x}

解答ステップ

\frac{d}{d x} (ln (4) lo g_{4} (x) + π^{3})

簡素化

ln (4) lo g_{4} (x) + π^{3} : ln (x) + π^{3}

= \frac{d}{d x} (ln (x) + π^{3})

和/差の法則を適用:

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

= \frac{d}{d x} (ln (x)) + \frac{d}{d x} (π^{3})

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

\frac{d}{d x} (π^{3}) = 0

= \frac{1}{x} + 0

簡素化

= \frac{1}{x}