derivative y=x^5log_{2}(x)

解

導関数

y = x^{5} lo g_{2} (x)

\frac{x ^{4} + 5 x ^{4} ln ( x )}{ln ( 2 )}

解答ステップ

\frac{d}{d x} (x^{5} lo g_{2} (x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{5}, g = lo g_{2} (x)

= \frac{d}{d x} (x^{5}) lo g_{2} (x) + \frac{d}{d x} (lo g_{2} (x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} lo g_{2} (x) + \frac{1}{x ln ( 2 )} x^{5}

簡素化

5 x^{4} lo g_{2} (x) + \frac{1}{x ln ( 2 )} x^{5} : \frac{x ^{4} + 5 x ^{4} ln ( x )}{ln ( 2 )}

= \frac{x ^{4} + 5 x ^{4} ln ( x )}{ln ( 2 )}