derivative of (log_{2}(x)^4)

解

\frac{d}{d x} ((lo g_{2} (x))^{4})

\frac{4 lo g _{2} ( x ) ^{3}}{ln ( 2 ) x}

解答ステップ

\frac{d}{d x} ((lo g_{2} (x))^{4})

連鎖法則を適用:

4 (lo g_{2} (x))^{3} \frac{d}{d x} (lo g_{2} (x))

= 4 (lo g_{2} (x))^{3} \frac{d}{d x} (lo g_{2} (x))

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

= 4 (lo g_{2} (x))^{3} \frac{1}{x ln ( 2 )}

簡素化

4 lo g_{2} (x)^{3} \frac{1}{x ln ( 2 )} : \frac{4 lo g _{2} ( x ) ^{3}}{ln ( 2 ) x}

= \frac{4 lo g _{2} ( x ) ^{3}}{ln ( 2 ) x}