derivative of x^2log_{2}(x^3)

解

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

\frac{3 x + 6 x ln ( x )}{ln ( 2 )}

解答ステップ

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

積の法則を適用:

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

f = x^{2}, g = lo g_{2} (x^{3})

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

簡素化

2 x lo g_{2} (x^{3}) + \frac{3}{ln ( 2 ) x} x^{2} : \frac{3 x + 6 x ln ( x )}{ln ( 2 )}

= \frac{3 x + 6 x ln ( x )}{ln ( 2 )}