derivative y=x^2ln(4x+3)

解

導関数

y = x^{2} ln (4 x + 3)

2 x ln (4 x + 3) + \frac{4 x ^{2}}{4 x + 3}

解答ステップ

\frac{d}{d x} (x^{2} ln (4 x + 3))

積の法則を適用:

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

f = x^{2}, g = ln (4 x + 3)

= \frac{d}{d x} (x^{2}) ln (4 x + 3) + \frac{d}{d x} (ln (4 x + 3)) x^{2}

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

\frac{d}{d x} (ln (4 x + 3)) = \frac{4}{4 x + 3}

= 2 x ln (4 x + 3) + \frac{4}{4 x + 3} x^{2}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 x ln (4 x + 3) + \frac{4 x ^{2}}{4 x + 3}